Existence of nonzero nonnegative solutions of semilinear equations at resonance

Michal Fečkan

Displaying similar documents to “Existence of nonzero nonnegative solutions of semilinear equations at resonance”

Existence of three solutions for sytems of multi-point boundary value problems.

Du, Zengji, Kong, Lingju (2009)

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

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Problems with nonlinear boundary value conditions

Michal Fečkan (1992)

Commentationes Mathematicae Universitatis Carolinae

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The existence and multiplicity results are shown for certain types of problems with nonlinear boundary value conditions.

Even periodic solutions of higher order duffing differential equations

Gen Qiang Wang, Sui-Sun Cheng (2007)

Czechoslovak Mathematical Journal

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By using Mawhin’s continuation theorem, the existence of even solutions with minimum positive period for a class of higher order nonlinear Duffing differential equations is studied.

Solvability of a higher-order multi-point boundary value problem at resonance

Xiaojie Lin, Qin Zhang, Zengji Du (2011)

Applications of Mathematics

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Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point boundary value problem at resonance $x^{(n)} (t) = f (t, x (t), x^{'} (t), \dots, x^{(n - 1)} (t)), t \in (0, 1), x (0) = \sum_{i = 1}^{m} α_{i} x (ξ_{i}), x^{'} (0) = \dots = x^{(n - 2)} (0) = 0, x^{(n - 1)} (1) = \sum_{j = 1}^{l} β_{j} x^{(n - 1)} (η_{j}),$ where $f : [0, 1] \times ℝ^{n} \to ℝ$ is a Carathéodory function, $0 < ξ_{1} < ξ_{2} < \dots < ξ_{m} < 1$ , $α_{i} \in ℝ$ , $i = 1, 2, \dots, m$ , $m \geq 2$ and $0 < η_{1} < \dots < η_{l} < 1$ , $β_{j} \in ℝ$ , $j = 1, \dots, l$ , $l \geq 1$ . In this paper, two of the boundary value conditions are responsible for resonance.