multiple solutions for biharmonic elliptic problems with the second hessian
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ID: 177383
2016
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Abstract
In this article, we study the biharmonic elliptic problem with
the secondnd Hessian
$$\displaylines{
\Delta^2u =S_2(D^2u)+\lambda f(x) |u|^{p-1}u,\quad \text{in }
\Omega \subset \mathbb{R}^3, \cr
u =\frac{\partial u}{\partial n}=0, \quad \text{on } \partial\Omega,
}$$
where $f(x)\in C(\bar{\Omega})$ is a sign-changing weight function.
By using variational methods and some properties of the Nehari manifold,
we prove that the biharmonic elliptic problem has at least two nontrivial
solutions.
| Reference Key |
fang2016electronicmultiple
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|---|---|
| Authors | ;Fei Fang;Chao Ji;Binlin Zhang |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2016 |
| DOI |
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