Yazar "Tokmak, Fatma" seçeneğine göre listele

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    Eigenvalues for iterative systems of nonlinear m-point boundary value problems on time scales
    (Springer International Publishing Ag, 2014) Karaca, Ilkay Y.; Tokmak, Fatma
    In this paper, we determine the eigenvalue intervals of the parameters lambda(1), lambda(2), ..., lambda(n) for which there exist positive solutions of the iterative systems of m-point boundary value problems on time scales. The method involves an application of Guo-Krasnosel'skii fixed point theorem. We give an example to demonstrate our main results.
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    Existence of Positive Solutions for Nonlinear Third-Order m-Point Boundary Value Problems on Time Scales
    (Univ Nis, Fac Sci Math, 2014) Karaca, Ilkay Yaslan; Tokmak, Fatma
    In this paper, we investigate the existence of double positive solutions for nonlinear third-order m-point boundary value problems with p-Laplacian on time scales. By using double fixed point theorem, we establish results on the existence of two positive solutions with suitable growth conditions imposed on the nonlinear term. As an application, we give an example to demonstrate our main result.
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    Existence of positive solutions for p-Laplacian impulsive boundary value problems on time scales
    (Springer International Publishing Ag, 2014) Tokmak, Fatma; Karaca, Ilkay Y.
    In this paper, by using fixed point index theory and a double fixed point theorem, we study the existence of many positive solutions for a class of second-order p-Laplacian boundary value problems with impulse on time scales. An example which supports our theoretical results is also indicated.
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    Existence of positive solutions for third-order boundary value problems with integral boundary conditions on time scales
    (Springeropen, 2013) Karaca, Ilkay Y.; Tokmak, Fatma
    In this paper, four functionals fixed point theorem is used to verify the existence of at least one positive solution for third-order boundary value problems with integral boundary conditions for an increasing homeomorphism and homomorphism on time scales. We also provide an example to demonstrate our results.
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    Existence of Positive Solutions for Third-Order m-Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales
    (Hindawi Publishing Corporation, 2012) Tokmak, Fatma; Karaca, Ilkay Yaslan
    A four-functional fixed point theorem and a generalization of Leggett-Williams fixed point theorem are used, respectively, to investigate the existence of at least one positive solution and at least three positive solutions for third-order m-point boundary value problem on time scales with an increasing homeomorphism and homomorphism, which generalizes the usual p-Laplacian operator. In particular, the nonlinear term f(t, u) is allowed to change sign. As an application, we also give some examples to demonstrate our results.
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    Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations with p-Laplacian Operator
    (Hindawi Ltd, 2014) Karaca, Ilkay Yaslan; Tokmak, Fatma
    This paper studies the existence of solutions for a nonlinear boundary value problem of impulsive fractional differential equations with p-Laplacian operator. Our results are based on some standard fixed point theorems. Examples are given to show the applicability of our results.
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    Existence of symmetric positive solutions for a multipoint boundary value problem with sign-changing nonlinearity on time scales
    (Springer International Publishing Ag, 2013) Tokmak, Fatma; Karaca, Ilkay Yaslan
    In this paper, we make use of the four functionals fixed point theorem to verify the existence of at least one symmetric positive solution of a second-order m-point boundary value problem on time scales such that the considered equation admits a nonlinear term f whose sign is allowed to change. The discussed problem involves both an increasing homeomorphism and homomorphism, which generalizes the p-Laplacian operator. An example which supports our theoretical results is also indicated. MSC: 34B10, 39A10.
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    Existence of symmetric positive solutions for a multipoint boundary value problem with sign-changing nonlinearity on time scales
    (Springer International Publishing Ag, 2013) Tokmak, Fatma; Karaca, Ilkay Yaslan
    In this paper, we make use of the four functionals fixed point theorem to verify the existence of at least one symmetric positive solution of a second-order m-point boundary value problem on time scales such that the considered equation admits a nonlinear term f whose sign is allowed to change. The discussed problem involves both an increasing homeomorphism and homomorphism, which generalizes the p-Laplacian operator. An example which supports our theoretical results is also indicated. MSC: 34B10, 39A10.
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    EXISTENCE OF THREE POSITIVE SOLUTIONS FOR M-POINT TIME SCALE BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS
    (Dynamic Publishers, Inc, 2011) Karaca, Ilkay Yaslan; Tokmak, Fatma
    In this paper, by using the Leggett-Williams fixed point theorem and Five Functionals fixed point theorem, we establish the existence of three positive solutions for at-point time scale boundary value problems on infinite intervals. As an application, we also give some examples to demonstrate our results.
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    Existence of three symmetric positive solutions for a second-order multi-point boundary value problem on time scales
    (Springer International Publishing Ag, 2014) Sinanoglu, Aycan; Karaca, Ilkay Y.; Tokmak, Fatma; Senlik, Tugba
    In this article, we investigate the existence of at least three symmetric positive solutions of a second-order multi-point boundary value problem on time scales. The ideas involve Bai and Ge's fixed point theorem. As an application, we give an example to demonstrate our main result.
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    Existence results for p-Laplacian boundary value problems of impulsive dynamic equations on time scales
    (Springer International Publishing Ag, 2013) Ozen, Ozlem B.; Karaca, Ilkay Y.; Tokmak, Fatma
    In this paper, Bai-Ge's fixed point theorem is used to investigate the existence of positive solutions for second-order boundary value problems of p-Laplacian impulsive dynamic equations on time scales. As an application, we give an example to demonstrate our results.
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    MULTIPLE POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR P-LAPLACIAN IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES
    (House Book Science-Casa Cartii Stiinta, 2014) Karaca, Ilkay Yaslan; Ozen, Ozlem Batit; Tokmak, Fatma
    In this paper, by using the classical fixed-point index theorem for compact maps and Leggett-Williams fixed point theorem, some sufficient conditions for the existence of multiple positive solutions for a class of second-order p-Laplacian boundary value problem with impulse on time scales are established. We also give an example to illustrate our results
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    Zaman skalasında bir boyutlu p- laplacian sınır değer problemlerinin pozitif çözümleri
    (Ege Üniversitesi, 2011) Tokmak, Fatma; Karaca, İlkay
    Bu tezde, diferansiyel denklemlerle ilgili birçok sonucun fark denklemleri ile es deger sonuçlara tasınabildigi zaman skalası üzerinde bazı temel özellikler verilmistir. Zaman skalasında delta ve nabla türevi içeren ikinci mertebeden bir boyutlu p-Laplacian sınır deger problemi ele alınmıs ve sonsuz aralıktaki zaman skalası üzerinde pozitif çözümlerinin varlıgı incelenmistir. Bunun için öncelikle koni, Banach uzayı, tamamen sürekli operatör ve fonksiyonel tanımları verilmistir. Ayrıca, sınır deger probleminin pozitif çözümlerinin varlıgı için gerekli teoremler verilmistir. Sırasıyla Leggett-Williams sabit nokta teoremi, Bes fonksiyonelli sabit nokta teoremi ve Bai ve Ge'nin ispatlamıs oldugu Leggett- Williams sabit nokta teoreminin bir genellestirilmisi ile en az üç pozitif çözümün varlıgı gösterilmis ve örneklendirilmistir.;Time scale, positive solutions, m-point boundary value problems, fixed point theorems, infinite intervals.;Zaman skalası, pozitif çözümler, m-nokta sınır deger problemleri, sabit nokta teoremleri, sonsuz aralık.
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    Zaman skalasında bir boyutlu p-Laplacian sınır değer problemlerinin pozitif çözümleri
    (Ege Üniversitesi, 2011) Tokmak, Fatma; Karaca, İlkay
    Bu tezde, diferansiyel denklemlerle ilgili birçok sonucun fark denklemleri ile eş değer sonuçlara taşınabildiği zaman skalası üzerinde bazı temel özellikler verilmiştir. Zaman skalasında delta ve nabla türevi içeren ikinci mertebeden bir boyutlu p-Laplacian sınır değer problemi ele alınmış ve sonsuz aralıktaki zaman skalası üzerinde pozitif çözümlerinin varlığı incelenmiştir. Bunun için öncelikle koni, Banach uzayı, tamamen sürekli operatör ve fonksiyonel tanımları verilmiştir. Ayrıca, sınır değer probleminin pozitif çözümlerinin varlığı için gerekli teoremler verilmiştir. Sırasıyla Leggett-Williams sabit nokta teoremi, Beş fonksiyonelli sabit nokta teoremi ve Bai ve Ge'nin ispatlamış olduğu Leggett-Williams sabit nokta teoreminin bir genelleştirilmişi ile en az üç pozitif çözümün varlığı gösterilmiş ve örneklendirilmiştir.