The main goal of the present paper is to prove the existence of saddle-type solutions for the following class of quasilinear problems $$ -\Delta_{\Phi}u + V'(u)=0\quad \text{in }\mathbb{R}^2, $$% where $$ \Delta_{\Phi}u=\text{div}(\phi(|\nabla u|)\nabla u), $$% $\Phi\colon \mathbb{R}\rightarrow [0,+\infty)$ is an N-function and the potential $V$ satisfies some technical condition and we have as an example $ V(t)=\Phi(|t^2-1|)$.
Existence of saddle-type solutions for a class of quasilinear problems in R^2 / Alves, Claudianor O.; Isneri, Renan J. S.; Montecchiari, Piero. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - 61:2(2023), pp. 825-868. [10.12775/TMNA.2022.039]
Existence of saddle-type solutions for a class of quasilinear problems in R^2
Montecchiari, Piero
2023-01-01
Abstract
The main goal of the present paper is to prove the existence of saddle-type solutions for the following class of quasilinear problems $$ -\Delta_{\Phi}u + V'(u)=0\quad \text{in }\mathbb{R}^2, $$% where $$ \Delta_{\Phi}u=\text{div}(\phi(|\nabla u|)\nabla u), $$% $\Phi\colon \mathbb{R}\rightarrow [0,+\infty)$ is an N-function and the potential $V$ satisfies some technical condition and we have as an example $ V(t)=\Phi(|t^2-1|)$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
