Multiple solutions to a boundary value problem for an n-th order nonlinear difference equation.

Lauer, Susan D.

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Existence of a positive solution for an $n$ th order boundary value problem for nonlinear difference equations.

Henderson, Johnny, Lauer, Susan D. (1997)

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Positive solutions to a boundary-value problem for second order ordinary differential equations.

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On a criterion for the existence of at least four solutions of functional boundary value problems

Staněk, Svatoslav (1997)

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A class of functional boundary conditions for the second order functional differential equation $x^{''} (t) = (F x) (t)$ is introduced. Here $F : C^{1} (J) \to L_{1} (J)$ is a nonlinear continuous unbounded operator. Sufficient conditions for the existence of at least four solutions are given. The proofs are based on the Bihari lemma, the topological method of homotopy, the Leray-Schauder degree and the Borsuk theorem.