Non-definite Sturm-Liouville problems for the p-Laplacian

Left-Definite Sturm-Liouville Problems

Left-definite regular self-adjoint Sturm-Liouville problems with separated and coupled boundary conditions are studied. A characterization is given in terms of right-definite problems, a concrete and “natural” indexing scheme for the eigenvalues is proposed. Pruefer transformation techniques can be used to establish the existence of and to give a characterization for the eigenvalues in the case...

Homotopy perturbation method for eigenvalues of non-definite Sturm-Liouville problem

In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.

Positive solutions for discrete Sturm-Liouville-like four-point p-Laplacian boundary value problems

We consider the existence of positive solutions for a class of discrete second-order four-point boundary value problem with p-Laplacian. Using the well known Krasnosel’skii’s fixed point theorem, some new existence criteria for positive solutions of the boundary value problem are presented.

Existence of Positive Solutions for Singular P-laplacian Sturm-liouville Boundary Value Problems

We prove the existence of positive solutions of the Sturm-Liouville boundary value problem −(r(t)φ(u′))′ = λg(t)f(t, u), t ∈ (0, 1), au(0)− bφ−1(r(0))u′(0) = 0, cu(1) + dφ−1(r(1))u′(1) = 0, where φ(u′) = |u′|p−2u′, p > 1, f : (0, 1) × (0,∞) → R satisfies a p-sublinear condition and is allowed to be singular at u = 0 with semipositone structure. Our results extend previously known results in the...

On the Nonhomogeneous Fourth-Order p-Laplacian Generalized Sturm-Liouville Nonlocal Boundary Value Problems