Problems with nonlinear boundary value conditions

Michal Fečkan

Displaying similar documents to “Problems with nonlinear boundary value conditions”

A third order nonlocal boundary value problem at resonance.

Kaufmann, Eric R. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Existence of nonzero nonnegative solutions of semilinear equations at resonance

Michal Fečkan (1998)

Commentationes Mathematicae Universitatis Carolinae

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The existence of nonzero nonnegative solutions are established for semilinear equations at resonance with the zero solution and possessing at most linear growth. Applications are given to nonlinear boundary value problems of ordinary differential equations.

Existence of solutions to a nonlocal boundary value problem with nonlinear growth.

Lin, Xiaojie (2011)

Boundary Value Problems [electronic only]

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Positive solutions for second-order three-point eigenvalue problems.

Bai, Chuanzhi (2010)

Abstract and Applied Analysis

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Solutions of a multi-point boundary value problem for higher-order differential equations at resonance. (II)

Yuji Liu, Weigao Ge (2005)

Archivum Mathematicum

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In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equation $x^{(n)} (t) = f (t, x (t), x^{'} (t), \dots, x^{(n - 1)} (t)) + e (t), 0 < t < 1, (*)$ and the following multi-point boundary value conditions $\begin{matrix} 1 * - 1 x^{(i)} (0) & = 0 f o r i = 0, 1, \dots, n - 3, \\ x^{(n - 1)} (0) & = α x^{(n - 1)} (ξ), x^{(n - 2)} (1) = \sum_{i = 1}^{m} β_{i} x^{(n - 2)} (η_{i}) . * * \end{matrix}$ Sufficient conditions for the existence of at least one solution of the BVP $(*)$ and $(* *)$ at resonance are established. The results obtained generalize and complement those in [13, 14]. This paper is directly motivated by Liu and Yu [J. Pure Appl. Math. 33 (4)(2002),...