On the existence of two solutions of functional boundary value problems
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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Department of Mathematical Analysis, Faculty of Science, Polacký University, Czech Republic Czechia
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