On the existence of two solutions of functional boundary value problems

Svatoslav Staněk

Published: 2022-07-23

Vol. 14 (2000)

On the existence of two solutions of functional boundary value problems

Svatoslav Staněk

Abstract

The functional differential equation (g(x'(t)))' = (Fx)(t) is considered. Here g is an increasing homomorphism on ℝ, g(0) = 0 and F: C¹(J)→L₁(J) is a continuous operator satisfying a growth condition with respect to x. A class of nonlinear functional boundary conditions is considered and sufficient conditions for the existence at least one positive and one negative solutions of the boundary value problems are given. Results are proved by the homotopy theory, the Leray-Schauder degree and the Borsuk theorem.

Keywords:

multiplicity , functional differential equation , functional boundary conditions , homotopy , Leray-Schauder degree , Borsuk theorem , p-Laplacian , Emden-Fowler equation

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Staněk, S. (2022). On the existence of two solutions of functional boundary value problems. Annales Mathematicae Silesianae, 14, 93–109. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14131

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Vol. 14 (2000)
Published: 2000-09-29

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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