existence of solutions to nonlocal kirchhoff equations of elliptic type via genus theory
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ID: 161210
2014
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Abstract
In this article, we study the existence and multiplicity of
solutions to the nonlocal Kirchhoff fractional equation
$$\displaylines{
\Big(a + b\int_{\mathbb{R}^{2N}} |u (x) - u (y)|^2 K (x - y)\,dx\,dy\Big)
(- \Delta)^s u - \lambda u = f (x, u (x)) \quad \text{in } \Omega,\cr
u = 0 \quad \text{in } \mathbb{R}^N \setminus \Omega,
}$$
where $a, b > 0$ are constants, $(- \Delta)^s$ is the fractional
Laplace operator, $s \in (0, 1)$ is a fixed real
number, $\lambda$ is a real parameter and $\Omega$ is an open bounded subset
of $\mathbb{R}^N$, $N > 2 s$, with Lipschitz boundary,
$f: \Omega \times \mathbb{R} \to \mathbb{R}$ is a continuous function.
The proofs rely essentially on the genus properties in critical point theory.
| Reference Key |
nyamoradi2014electronicexistence
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|---|---|
| Authors | ;Nemat Nyamoradi;Nguyen Thanh Chung |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2014 |
| DOI |
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| URL | |
| Keywords | Keywords not found |
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