Electron. J. Differential Equations,
Vol. 2017 (2017), No. 206, pp. 120.
Fractional elliptic systems with nonlinearities
of arbitrary growth
Edir Junior Ferreira Leite
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
in
:
where
and
denote spectral fractional
Laplace operators. We assume that
, and the function
f is superlinear and with no growth restriction (for example
);
thus the system has a nontrivial solution. Another important example is given
by
.
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
Submitted June 10, 2017. Published September 7, 2017.
Math Subject Classifications: 35J65, 49K20, 35J40.
Key Words: Fractional elliptic systems; critical growth; critical hyperbola.
Show me the PDF file (320 KB),
TEX file for this article.

Edir Junior Ferreira Leite
Departamento de Matemática
Universidade Federal de Viçosa
CCE, 36570000, Viçosa, MG, Brazil
email: edirjrleite@ufv.br

Return to the EJDE web page