Yazar "Agarwal, Ravi P." seçeneğine göre listele

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    Existence Criteria of Positive Solutions for Fractional p-Laplacian Boundary Value Problems
    (Univ Nis, Fac Sci Math, 2020) Deren, Fulya Yoruk; Cerdik, Tugba Senlik; Agarwal, Ravi P.
    By means of the Bai-Ge's fixed point theorem, this paper shows the existence of positive solutions for nonlinear fractional p-Laplacian differential equations. Here, the fractional derivative is the standard Riemann-Liouville one. Finally, an example is given to illustrate the importance of results obtained.
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    Existence of positive solutions for Lidstone boundary value problems on time scales
    (Springer, 2023) Cetin, Erbil; Topal, Fatma Serap; Agarwal, Ravi P.
    Let T subset of R be a time scale. The purpose of this paper is to present sufficient conditions for the existence of multiple positive solutions of the following Lidstone boundary value problem on time scales: (-1)(n)y(Delta(2n)) (t) = f (t, y(t)), t is an element of [a, b]T, y(Delta(2i)) (alpha) = y(Delta(2i)) (sigma(2n-2i)(b)) i = 0, i = 0,1,..., n - 1. Existence of multiple positive solutions is established using fixed point methods. At the end some examples are also given to illustrate our results.
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    Existence of solutions for fourth order three-point boundary value problems on a half-line
    (Univ Szeged, Bolyai Institute, 2015) Cetin, Erbil; Agarwal, Ravi P.
    In this paper, we apply Schauder's fixed point theorem, the upper and lower solution method, and topological degree theory to establish the existence of unbounded solutions for the following fourth order three-point boundary value problem on a half-line x''''(t) + q(t) f(t, x(t), x'(t), x ''(t), x'''(t)) = 0, t is an element of (0, +infinity), x ''(0) = A, x(eta) = B-1, x'(eta) = B-2, x'''(+infinity) = C, where eta is an element of (0, +infinity), but fixed, and f : [0, +infinity) x R-4 -> R satisfies Nagumo's condition. We present easily verifiable sufficient conditions for the existence of at least one solution, and at least three solutions of this problem. We also give two examples to illustrate the importance of our results.
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    Existence of solutions to fourth-order differential equations with deviating arguments
    (Springeropen, 2015) Naceri, Mostepha; Agarwal, Ravi P.; Cetin, Erbil; Amir, El Haffaf
    In this paper, we consider fourth-order differential equations on a half-line with deviating arguments of the form u((4))(t) + q(t) f (t, [u(t)], [u'(t)], [u ''(t)], u'''(t)) = 0, 0 < t < + infinity, with the boundary conditions u(0) = A, u' (0) = B, u '' (t) -au'''(t) = theta(t), -tau <= t <= 0; u'''(+infinity) = C. We present sufficient conditions for the existence of a solution between a pair of lower and upper solutions by using Schauder's fixed point theorem. Also, we establish the existence of three solutions between two pairs of lower and upper solutions by using topological degree theory. An important feature of our existence criteria is that the obtained solutions may be unbounded. We illustrate the importance of our results through two simple examples.
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    Existence of solutions to fourth-order differential equations with deviating arguments
    (Springeropen, 2015) Naceri, Mostepha; Agarwal, Ravi P.; Cetin, Erbil; Amir, El Haffaf
    In this paper, we consider fourth-order differential equations on a half-line with deviating arguments of the form u((4))(t) + q(t) f (t, [u(t)], [u'(t)], [u ''(t)], u'''(t)) = 0, 0 < t < + infinity, with the boundary conditions u(0) = A, u' (0) = B, u '' (t) -au'''(t) = theta(t), -tau <= t <= 0; u'''(+infinity) = C. We present sufficient conditions for the existence of a solution between a pair of lower and upper solutions by using Schauder's fixed point theorem. Also, we establish the existence of three solutions between two pairs of lower and upper solutions by using topological degree theory. An important feature of our existence criteria is that the obtained solutions may be unbounded. We illustrate the importance of our results through two simple examples.
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    Existence of solutions to fourth-order differential equations with deviating arguments
    (Springeropen, 2015) Naceri, Mostepha; Agarwal, Ravi P.; Cetin, Erbil; Amir, El Haffaf
    In this paper, we consider fourth-order differential equations on a half-line with deviating arguments of the form u((4))(t) + q(t) f (t, [u(t)], [u'(t)], [u ''(t)], u'''(t)) = 0, 0 < t < + infinity, with the boundary conditions u(0) = A, u' (0) = B, u '' (t) -au'''(t) = theta(t), -tau <= t <= 0; u'''(+infinity) = C. We present sufficient conditions for the existence of a solution between a pair of lower and upper solutions by using Schauder's fixed point theorem. Also, we establish the existence of three solutions between two pairs of lower and upper solutions by using topological degree theory. An important feature of our existence criteria is that the obtained solutions may be unbounded. We illustrate the importance of our results through two simple examples.
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    Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales
    (Springer-Verlag Italia Srl, 2017) Agarwal, Ravi P.; Cetin, Erbil; Ozbekler, Abdullah
    In this paper, we present some newHartman and Lyapunov inequalities for second-order forced dynamic equations on time scales T with mixed nonlinearities: x(Delta Delta)(t) + Sigma(n)(k=1) qk (t)vertical bar x(sigma) (t)vertical bar (alpha k-1) x(sigma) (t) = f (t); t is an element of [t(0), infinity)(T), where the nonlinearities satisfy 0 < alpha(1) < ... < alpha(m) < 1 < alpha(m+1) < ... < alpha(n) < 2. No sign restrictions are imposed on the potentials qk, k = 1, 2, ... , n, and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.
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    New uniqueness results for fractional differential equations
    (Taylor & Francis Ltd, 2013) Yoruk, Fulya; Bhaskar, T. Gnana; Agarwal, Ravi P.
    We develop the KrasnoselskiiKrein type of uniqueness theorem for an initial value problem of the RiemannLiouville type fractional differential equation which involves a function of the form f?(t,?x(t),?D q-1 x(t)), for 1
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    New uniqueness results for fractional differential equations
    (Taylor & Francis Ltd, 2013) Yoruk, Fulya; Bhaskar, T. Gnana; Agarwal, Ravi P.
    We develop the KrasnoselskiiKrein type of uniqueness theorem for an initial value problem of the RiemannLiouville type fractional differential equation which involves a function of the form f?(t,?x(t),?D q-1 x(t)), for 1
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    Unbounded solutions of third order three-point boundary value problems on a half-line
    (Walter De Gruyter Gmbh, 2016) Agarwal, Ravi P.; Cetin, Erbil
    We consider the following third order three-point boundary value problem on a half-line: x '''(t) + q(t)f(t, x(t), x'(t), x ''(t)) = 0, t is an element of (0, +infinity), x '(0) = A, x(eta) = B, x ''(+infinity) = C, where eta is an element of (0, +infinity), but fixed, and f : [0, +infinity) x R-3 -> R satisfies Nagumo's condition. We apply Schauder's fixed point theorem, the upper and lower solution method, and topological degree theory, to establish existence theory for at least one unbounded solution, and at least three unbounded solutions. To demonstrate the usefulness of our results, we illustrate two examples.