Nontrivial solutions of singular superlinear Sturm–Liouville problems

Nontrivial Solutions for Singular Nonlinear Three-Point Boundary Value Problems

The singular nonlinear three-point boundary value problems { −(Lu)(t) = h(t)f (u(t)), 0 < t < 1, βu(0)− γ u′(0) = 0, u(1) = αu(η) are discussed under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, where (Lu)(t) = (p(t)u′(t))′+q(t)u(t), 0 < η < 1, h(t) is allowed to be singular at both t = 0 and t = 1, and f need not be nonnegative. The associated ...

Nontrivial Solutions of p-Superlinear p-Laplacian Problems via a Cohomological Local Splitting

We consider a quasilinear equation, involving the p-Laplace operator, with a p-superlinear nonlinearity. We prove the existence of a nontrivial solution, also when there is no mountain pass geometry, without imposing a global sign condition. Techniques of Morse theory are employed.

Superlinear Singular Problems on the Half Line

Copyright q 2010 I. Rachůnková and J. Tomeček. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The paper studies the singular differential equation p t u′ ′ p t f u , which has a singularity at t 0. Here the existence of strictly ...

Nontrivial solutions of Kirchhoff type problems

In this paper, we study Kirchhoff type problems on a bounded domain. We consider the cases that the nonlinearity is superlinear near zero but asymptotically 4-linear at infinity, and the nonlinearity is asymptotically linear near zero but 4-superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.

An Existence Result of Positive Solutions for Singular Superlinear Boundary Value Problems and Its Applications