Akademik Bilgiler



İLKAY KARACA
PROFESÖR
Fen Fakültesi
Matematik Bölümü
Analiz ve Fonksiyonlar Teorisi Ana Bilim Dalı
İletişim Bilgileri- E-posta: ilkay.karaca@ege.edu.tr
Eğitim Bilgileri- Lisans: Ege Üniversitesi, Türkiye, 1989
- Yüksek Lisans: Ege Üniversitesi, Türkiye, 1993
- Doktora: Ege Üniversitesi, Türkiye, 1996
- Yardımcı Doçentlik: Ege Üniversitesi, Türkiye, 1997
- Doçentlik: Ege Üniversitesi, Türkiye, 2008
- Profesörlük: Ege Üniversitesi, Türkiye , 2015

İndekslerce Taranan Dergilerdeki Yayınları (57 adet)- Çerdik,T. Senlik, Karaca, I. Yaslan, Sinanoglu A. and Fen, F. Tokmak, On the Solvability of a System of Multi-Point Second Order Boundary Value Problem, Journal of Computational Analysis and Applications 20 (2016) 666-673.
- Fen, F. Tokmak, Karaca, I. Yaslan, Existence of Positive Solutions for Nonlinear Second-Order Impulsive Boundary Value Problems on Time Scales, Mediterranian Journal of Mathematics 13 (2016) 191-204.
- Fen, F. Tokmak and Karaca, I. Yaslan, On positive solutions of m-point boundary value problems for p-Laplacian impulsive dynamic equations on time scales, Indian Journal of Pure and Applied Mathematics 46 (2015) 723-738.
- Karaca, I. Yaslan and Fen, F.Tokmak, Positive Solutions of nth-Order Boundary Value Problems with Integral Boundary Conditions, Mathematical Modelling and Analysis 20 (2015) 188-204.
- Tokmak, F., Karaca, I. Yaslan, Senlik T. and Sinanoglu, A., The Existence of Symmetric Positive Solutions for a Nonlinear Multi-Point Boundary Value Problem on Time Scales, Journal of Computational Analysis and Applications 19 (2015) 670-677.
- Karaca, I. Yaslan, On positive solutions for fouth-order four-point boundary value problems with alternating coefficient on time scales, Dynamic Systems and Applications 24 (2015) 313-326.
- Karaca, I. Yaslan and Fen, F. Tokmak, Positive solutions of nth-order m-point impulsive boundary value problems, Georgian Mathematical Journal 22 (2015) 373-384.
- Karaca, I. Yaslan and Fen, F. Tokmak, Multiple positive solutions for nonlinear second-order m-point impulsive boundary value problems on time scales, Filomat 29 (2015) 817-827.
- Karaca, I. Yaslan and Fen, F.Tokmak, Eigenvalues for iterative systems of dynamic equations with integral boundary conditions on time scales, Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Istatistics 64 (2015) 87-97.
- Fen, F. Tokmak and Karaca, I. Yaslan, Nonlinear four-point impulsive fractional differential equations with p-Laplacian operator, Discontinuity, Nonlinearity, and Complexity 4(4) (2015) 467-486.
- Karaca, I. Yaslan, Ozen, Ozlem Batit and Tokmak F., Multiple positive solutions of boundary value problems for p-Laplacian impulsive dynamic equations on time scales, Fixed Point Theory, 15 (2014) 475-486.
- Sinanoglu, A., Karaca, I. Yaslan, Tokmak, F. and Senlik, T., Existence of Three Symmetric Positive Solutions for a Second-Order Multi-Point Boundary Value Problem on Time Scales, Advances in Difference Equations, 2014, 2014:81, doi:10.1186/1687-1847-2014-81.
- Karaca, I. Yaslan and Tokmak F., Existence of positive solutions for nonlinear third-order m-point boundary value problems on time scales, Filomat, 28:5 (2014) 925–935.
- Tokmak, F. and Karaca, I. Yaslan, Existence of Positive Solutions for a Second- Order Eigenvalue Boundary Value Problem with Impulse on Time Scales, Journal of Advanced Research in Applied Mathematics, 6 (2014) 32-49.
- Karaca, I. Yaslan and Tokmak, F., Existence of solutions for nonlinear impulsive fractional di erential equations with p-Laplacian operator, Mathematical Problems in Engineering, Volume 2014, Article ID 692703, 11 pages.
- Karaca, I. Yaslan and Tokmak, F., Eigenvalues for Iterative Systems of Nonlinear m-point Boundary Value Problems on Time Scales, Boundary Value Problems, 2014, 2014:63, doi:10.1186/1029-242X-2013-498.
-  Karaca, I. Yaslan and Tokmak, F., Positive solutions of nth-order impulsive differential equations with integral boundary conditions, Analele Univ. “Ovidius”, Math Series, 2014
- Tokmak, F. and Karaca, I. Yaslan, Existence of Positive Solutions for $p$-Laplacian Impulsive Boundary Value Problems on Time Scales, Journal of Inequalities and Applications, 2014, 2014:196, doi:10.1186/1687-2770-2014-63.
- Fen, F. Tokmak and Karaca, I. Yaslan, Existence of positive solutions for boundary value problems of p-Laplacian difference equations, Advances in Difference Equations, 2014:263.
- Karaca, I. Yaslan and Fen, F. Tokmak, Positive Solutions of Boundary Value Problems for Second-order p-Laplacian Difference Equations,International Journal of Difference Equations 9 (2014) 243–269.
- Karaca, I. Yaslan, On positive solutions for second-order boundary value problems of functional differential equations, Appl. Math. Comput. 219 (2013) 5433–5439.
- Karaca, I. Yaslan, Positive solutions to a nonlinear 2nth order boundary value problems on time scales, J. Comput. Anal. Appl. 15 (2013) 604-611.
- Karaca, I. Yaslan, Positive solutions of an nth order three-point boundary value problem, Rocky Mountain Journal of Mathematics, 43 (2013) 205-224.
- Tokmak, F. and Karaca, I. Yaslan, Existence of symmetric positive solutions for a multipoint boundary value problem with sign-changing nonlinearity on time scales, Boundary Value Problems 2013, 2013:52 doi:10.1186/1687-2770-2013-52.
- Tokmak, F., Karaca, I. Yaslan, Positive solutions of an impulsive second-order boundary value problem on time scales, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 20 (2013) 695-708.
- Tokmak, F., Karaca, I. Yaslan, Positive solutions for second order multi-point boundary value problems, Chaotic Modeling and Simulation, 3 (2013) 463-471.
- Karaca, I. Yaslan, Tokmak, F., Existence of positive solutions for third-order boundary value problems with integral boundary conditions on time scales, Journal of Inequalities and Applications, 2013, 2013:298.
- Ozen, Ozlem B., Karaca, I. Yaslan, Tokmak, F., Existence results for p- Laplacian boundary value problems of impulsive dynamic equations on time scales, Advances in Difference Equations, 2013, 2013:334.
- Ozen, Ozlem B., Karaca, I. Yaslan, Existence of solutions for m-point boundary value problem with p- Laplacian on time scales, Nonlinear Dynamics and Systems Theory, 13 (2013) 270-285.
- Karaca, I. Yaslan, Positive solutions of an nth order multi-point boundary value problem, J. Comput. Anal. Appl. 14 (2012) 181-193.
- Karaca, I. Yaslan, Upper and Lower Solution Method for Fourth-Order Four-Point Boundary Value Problem on Time Scales, Abstr. and Appl. Anal. Article ID 647235 (2012) 1-14.
- Tokmak, F. and Karaca, I. Yaslan, Existence of Positive Solutions for Third-Order m-Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales, Abstr. and Appl. Anal. Article ID 506716 (2012) 1-15.
- Karaca, I. Yaslan and Tokmak F., Triple positive solutions of m-point time scale BVPs with p-Laplacian on infinite intervals, Dynamic Systems and Applications 6 (2012) 205–212.
- Karaca, I. Yaslan, Positive solutions to a system of a boundary value problems for higher-dimensional dynamic equations on time scales, The Australian Journal of Mathematical Analysis and Applications, 9 (2012) 1-13.
- Karaca, I. Yaslan and Tokmak, F., Existence of three positive solutions for m-point time scale boundary value problems on infinite intervals, Dynam. Systems and Appl. 20 (2011) 355-367.
-  Karaca, I. Yaslan, Positive solutions to an nth order multi-point boundary value problem on time scales, Nonlinear Dyn. Syst. Theory 11 (2011) 285–296.
- Karaca, I. Yaslan and Yılmaz, O., Fourth-order m-point boundary value problems on time scales, Dynam. Systems and Appl. 19 (2010) 249-270.
- Karaca, I. Yaslan, On positive solutions for higher-order boundary value problems with impulse, Dynam. Systems and Appl. 18 (2009) 687-700.
- Karaca, I. Yaslan, Positive solutions for boundary value problems of second-order functional dynamic equations on time scales, Adv. Difference Equ. (2009), Article ID 829735, pages 1-21.
- Karaca, I. Yaslan, On positive solutions for fourth-order boundary value problem with impulse, J. Comput. Appl. Math. 225 (2009) 356-364.
- Karaca, I. Yaslan, Asymptotic formulas for eigenvalues of a Hill's equation with piecewise constant coefficient, Math. Proc. R. Ir. Acad. 109 (2009) 19-34.
- Anderson, D.R. and Karaca, I. Yaslan, Higher order three point boundary value problem on time scales, Comput. Math. Appl. 56 (2008) 2429-2443.
- Karaca, I. Yaslan, Fourth-order four-point boundary value problem on time scales, Appl. Math. Lett. 21 (2008) 1057-1063.
- Karaca, I. Yaslan, Multiple positive solutions for dynamic m-point boundary value problems, Dynam. Systems Appl. 17 (2008) 25-42.
- Karaca, I. Yaslan, Nonlinear triple-point problems with change of sign, Comput. Math. Appl. 55 (2008) 691-703.
- Karaca, I. Yaslan, On the existence of positive solutions for three-point boundary value problems with alternating coefficients, Math. Comput. Modelling 47 (2008) 1019-1034.
- Karaca, I. Yaslan, Discrete third-order three-point boundary value problem, J. Comput. Appl. Math. 205 (2007) 458-468.
- Karaca, I. Yaslan, Positive solutions to nonlinear three point boundary value problems on time scales, PanAmerican J.Mathematics 17 (2007) 33-49.
-  Karaca, I. Yaslan, On Hill's equation with piecewise constant and alternating coefficient, Journal of Science and Tecnology 1 (2007) 157-266.
- Karaca, I. Yaslan, Existence and nonexistence of positive solution to a right-focal boundary problem on time scale, Adv. Difference Equ. (2006) Article ID 43039, pages 1-13.
- Karaca, I. Yaslan ve G. Sh. Guseinov, Instability intervals of a Hill's equation with piecewise constant and alternating coefficient, Comput. Math. Appl. 47 (2004), 319-326.
- Karaca, I. Yaslan, On instability intervals of the Hill's equation with piecewise continuous coefficient, PanAmerican J.Mathematics 13 (2003) 89-98.
- Karaca, I. Yaslan, On Hill's equation with a discontinuous coefficient, Int. J. Mathematics and Mathematical Science 25 (2003) 1599-1624.
-  Karaca, I. Yaslan and Karaca I., Some formulas for conjugation, Southwest J. Pure and Applied Mathematics 2 (2001) 43-52.
-  Karaca, I. Yaslan and Karaca I., On conjugation in the mod-p Steenrod algebra, Turkish J. Mathematics 24-48 (2001) 1-7.
- Yaslan, I., On the lengths of the instability intervals of Hill's equation with a piecewise constant coefficient, J. of Faculty of Sciences Ege University, 21-28 (1998) 85-92.
- Yaslan I. and G. Sh. Guseinov, On Hill's equation with piecewise constant coefficient, Turkish J. Mathematics 21-4 (1997) 461-474.

İndekslerce Taranmayan Dergilerdeki Yayınları (1 adet)- Tokmak, F. and Karaca, I. Yaslan, Positive solutions for third-order m-point boundary value problems for an increasing homeomorphism and homomorphism with sign changing nonlinearity on time scales, 2nd International Symposium on Computing in Science&Engineering 700 (2011)1089-1095.

Diğer Dergiler ve Medyalardaki Yayınları (2 adet)- 0, Yüksek Lisans Tezi, Distribüsyon Uzayları ve Bazı Konvolüsyon Denklemlerinin Distribüsyon Çözümlerinin Araştırılması, 1993.
- 0, Doktora Tezi, Periyodik ve Süreksiz Fonksiyon Katsayılı Sturm-Liouville Denkleminin Spektral Teorisi Üzerine, 1996.

Uluslararası Toplantılarda Sunulan Bildirileri (4 adet)- Saçıkara, E. and Karaca, I. Yaslan, Existence of positive solutions for m-point boundary value problem with sign changing nonlinearity on time scales, International Conference on Applied Analysis and Algebra, Yildiz Technical University, Istanbul, Turkey, 2012.
- Tokmak, F. and Karaca, I. Yaslan, A note on unbounded positive solutions for m-point time-scale boundary value problems on infinite intervals, International Conference on Applied Analysis and Algebra, Yildiz Technical University, Istanbul, Turkey, 2012.
- Tokmak, F. and Karaca, I. Yaslan, Existence of three positive solutions for m-point time scale boundary value problems on infinite intervals, The Sixth International Conference on Dynamic Systems and Applications, Morehouse College, Atlanta, Georgia, U.S.A., 2011.
- Tokmak, F. and Karaca, I. Yaslan, Positive solutions for third-order m-point boundary value problems for an increasing homeomorphism and homomorphism with sign changing nonlinearity on time scales, 2nd International Symposium on Computing in Science&Engineering, Kuşadası, Aydın, Turkey, 2011.

Ulusal Toplantılarda Sunulan Bildirileri (3 adet)- Yaslan, I., On the instability intervals of Hill’s equation with discontinuous coefficient, 9th National Mathematic Symposium, Istanbul, 1996.
- Yaslan, I., On the instability intervals of Hill’s equation, Mathematic Symposium, Altinoluk, 1996.
- Yaslan, I., On the Hill’s equation with discontinuous coefficient, 8nd National Mathematic Symposium, Adana, 1995.

Tamamlanmış Araştırma Projeleri (6 adet)- 2012, Araştırma Projesi, Karaca, I. Yaslan and Saçıkara, E., Zaman skalasında sonsuz aralık üzerinde ikinci mertebeden sınır değer problemlerinin pozitif çözümleri, 11 Fen 066, Ege University.
- 2012, Araştırma Projesi, Karaca, I. Yaslan and Sinanoğlu, A., Zaman skalasında dördüncü mertebeden sınır değer problemlerinin simetrik pozitif çözümleri, 11 Fen 095, Ege University.
- 2011, Araştırma Projesi, Karaca, I. Yaslan and Tokmak, F., Zaman skalasında bir boyutlu p-laplacian sınır değer problemlerinin pozitif çözümleri, 2010 Fen 050, Ege University.
- 2010, Araştırma Projesi, Karaca, I. Yaslan, Positive solutions to higher order boundary value problems on time scales, 2009 Science 053, Ege University.
- 2008, Araştırma Projesi, Karaca, I. Yaslan and Yılmaz, Fourth-order m-point boundary value problems on time scales, Ilkay Karaca and Ozlem Yılmaz, 2007 Science 008, Ege University.
- 2005, Araştırma Projesi, Existence and nonexistence of positive solutions to a right-focal boundary value problem on time scales, Ilkay Karaca, 2004 Science 043, Ege University.
Yöneterek Sonuçlandırdığı Öğrenci Tezleri (5 adet)- Yüksek Lisans, 2012, Saçıkara, Elif, Zaman skalasında sonsuz aralık üzerinde ikinci mertebeden sınır değer problemlerinin pozitif çözümleri.
- Yüksek Lisans, 2012, Sinanoğlu, Aycan, Zaman skalasında dördüncü mertebeden sınır değer problemlerinin simetrik pozitif çözümleri.
- Yüksek Lisans, 2011, Tokmak, Fatma, Zaman skalasında bir boyutlu p-laplacian sınır değer problemlerinin pozitif çözümleri.
- Yüksek Lisans, 2008, Yılmaz, Özlem, Fourth-order m-point boundary value problems on time scales.
- Yüksek Lisans, 2005, Sevilcan, Hande Özsümer, Positive solutions of the second-order two-point boundary value problems on time scales.