fractional elliptic systems with nonlinearities of arbitrary growth
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ID: 167284
2017
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Abstract
In this article we discuss the existence, uniqueness and regularity
of solutions of the following system of coupled semilinear Poisson
equations on a smooth bounded domain $\Omega$ in $\mathbb{R}^n$:
$$\displaylines{
\mathcal{A}^s u= v^p \quad\text{in }\Omega\cr
\mathcal{A}^s v = f(u) \quad\text{in }\Omega\cr
u= v=0 \quad\text{on }\partial\Omega
}$$
where $s\in (0, 1)$ and $\mathcal{A}^s$ denote spectral fractional
Laplace operators. We assume that $1< p<\frac{2s}{n-2s}$, and the function
f is superlinear and with no growth restriction (for example $f(r)=re^r$);
thus the system has a nontrivial solution. Another important example is given
by $f(r)=r^q$. In this case, we prove that such a system admits at least one
positive solution for a certain set of the couple (p,q) below the critical
hyperbola
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| Reference Key |
leite2017electronicfractional
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|---|---|
| Authors | ;Edir Junior Ferreira Leite |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2017 |
| DOI |
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| URL | |
| Keywords | Keywords not found |
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