fractional elliptic systems with nonlinearities of arbitrary growth

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ID: 167284
2017
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Ranked #139 of 219 articles by views in icsoft 2006 - 1st international conference on software and data technologies, proceedings

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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
Reference Key
leite2017electronicfractional Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Edir Junior Ferreira Leite
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Journal icsoft 2006 - 1st international conference on software and data technologies, proceedings
Year 2017
DOI
DOI not found
URL
http://ejde.math.txstate.edu/Volumes/2017/206/abstr.html
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