Search results for " variational method"
showing 3 items of 13 documents
Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems
2017
We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…
Existence of three solutions for a mixed boundary value system with (p_1,...,p_m)-Laplacian
2014
In this paper we prove the existence of at least three weak solutions for a mixed boundary value system with (p_1,,...,p_m)-Laplacian. The approach is based on variational methods.
Two positive solutions for a nonlinear parameter-depending algebraic system
2021
The existence of two positive solutions for a nonlinear parameter-depending algebraic system is investigated. The main tools are a finite dimensional version of a two critical point theorem and a recent weak-strong discrete maximum principle.