first curve of fucik spectrum for the p-fractional laplacian operator with nonlocal normal boundary conditions
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ID: 152677
2018
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Abstract
In this article, we study the Fucik spectrum of the p-fractional
Laplace operator with nonlocal normal derivative conditions which
is defined as the set of all $(a,b)\in\mathbb{R}^2$ such that
$$\displaylines{
\Lambda_{n,p}(1-\alpha)(-\Delta)_{p}^{\alpha} u
+ |u|^{p-2}u = \frac{\chi_{\Omega_\epsilon}}{\epsilon} (a (u^{+})^{p-1}
- b (u^{-})^{p-1}) \quad \text{in }\Omega, \cr
\mathcal{N}_{\alpha,p} u = 0 \quad \text{in }\mathbb{R}^n \setminus
\overline{\Omega},
}$$
has a non-trivial solution u, where $\Omega$ is a bounded domain in
$\mathbb{R}^n$ with Lipschitz boundary, $p \geq 2$, $n>p \alpha$,
$\epsilon, \alpha \in(0,1)$ and
$\Omega_{\epsilon}:=\{x \in \Omega: d(x,\partial \Omega)\leq \epsilon \}$.
We show existence of the first non-trivial curve $\mathcal{C}$ of the
Fucik spectrum which is used to obtain the variational
characterization of a second eigenvalue of the problem defined above.
We also discuss some properties of this curve $\mathcal{C}$,
e.g. Lipschitz continuous, strictly decreasing
and asymptotic behavior and non-resonance with respect to the
Fucik spectrum.
| Reference Key |
goel2018electronicfirst
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|---|---|
| Authors | ;Divya Goel;Sarika Goyal;Konijeti Sreenadh |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2018 |
| DOI |
DOI not found
|
| URL | |
| Keywords | Keywords not found |
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