Existence of saddle-type solutions for a class of quasilinear problems in R^2
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Published:2023-07-16
Issue:
Volume:
Page:1-44
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ISSN:1230-3429
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Container-title:Topological Methods in Nonlinear Analysis
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language:
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Short-container-title:TMNA
Author:
Alves Claudianor O.,Isneri Renan J. S.,Montecchiari Piero
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|)$.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Subject
Applied Mathematics,Analysis
Cited by
1 articles.
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