Exact number of pseudo-symmetric positive solutions for a p-Laplacian three-point boundary value problems and their applications

Abstract

In this paper, the exact number of pseudo-symmetric positive solutions is obtained for a class of three-point boundary value problems with one-dimensional p-Laplacian. The interesting point is that the nonlinearity f is general form: f (u) = λg(u) + h(u). Meanwhile, some properties of the solutions are given in details. The arguments are based upon a quadrature method.

Existence and Multiplicity Results for Nonlocal Boundary Value Problems with Strong Singularity

“…Indeed, assume on the contrary that β does not satisfy (18), i.e., there exists t 0 ∈ (0, 1) such that…”

“…which contradicts the choice of . Thus, β(t) = u 1 (t) + δ satisfies (18). Consider the following modified problem…”