Multiple sign-changing solutions for Kirchhoff type problems
This article concerns the existence of sign-changing solutions to nonlocal Kirchhoff type problems of the form $$ -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) \text{ in }\Omega,\quad u=0 \text{ on }\partial\Omega, $$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$ ($N=1,2,3$)...
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Format: | Article |
Language: | English |
Published: |
Texas State University
2016-06-01
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Series: | Electronic Journal of Differential Equations |
Subjects: | |
Online Access: | http://ejde.math.txstate.edu/Volumes/2016/135/abstr.html |
Summary: | This article concerns the existence of sign-changing solutions
to nonlocal Kirchhoff type problems of the form
$$
-\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) \text{ in }\Omega,\quad
u=0 \text{ on }\partial\Omega,
$$
where $\Omega$ is a bounded domain in $\mathbb{R}^N$ ($N=1,2,3$)
with smooth boundary, $a>0$, $b\geq0$, and
$f:\overline{\Omega}\times\mathbb{R}\to\mathbb{R}$ is a continuous function.
We first establish a new sign-changing version of the symmetric mountain
pass theorem and then apply it to prove the existence of a sequence of
sign-changing solutions with higher and higher energy. |
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ISSN: | 1072-6691 |