Search results for "Three solutions"

Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian

2004

AbstractThis paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93–104].

Superlinear Robin Problems with Indefinite Linear Part

2018

We consider a semilinear Robin problem with an indefinite linear part and a superlinear reaction term, which does not satisfy the usual in such cases AR condition. Using variational methods, together with truncation–perturbation techniques and Morse theory (critical groups), we establish the existence of three nontrivial solutions. Our result extends in different ways the multiplicity theorem of Wang.

A Mountain Pass Theorem for a Suitable Class of Functions

2009

Three solutions for a Neumann boundary value problem involving the p-Laplacian

2005

In this note we prove the existence of an open interval ]λ', λ"[ for each λ of which a Neumann boundary value problem involving the p-Laplacian and depending on λ admits at least three solutions. The result is based on a recent three critical points theorem.