Edir Junior Ferreira Leite
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.
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| Edir Junior Ferreira Leite |
Departamento de Matemática
Universidade Federal de Viçosa
CCE, 36570-000, Viçosa, MG, Brazil
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