Minimax Theory and its Applications 04 (2019), No. 1, 101--112
Copyright Heldermann Verlag 2019
Multiple Entire Solutions for Schrödinger-Hardy Systems Involving Two Fractional Operators
Alessio Fiscella
Departamento de Matemática, Universidade Estadual de Campinas, Rua S. Buarque de Holanda 651, Campinas - CEP 13083-859, Brazil
fiscella@ime.unicamp.br
[Abstract-pdf]
The paper is devoted to the study of the following fractional Schr\"odinger-Hardy system in $\mathbb R^n$ $$ \left\{\begin{aligned} &(-\Delta)^{s}_mu+a(x)|u|^{m-2}u-\mu\frac{|u|^{m-2}u}{|x|^{ms}}=H_u(x,u,v),\\ &(-\Delta)^s_p v+b(x)|v|^{p-2}v-\sigma\,\frac{|v|^{p-2}v}{|x|^{ps}}=H_v(x,u,v), \end{aligned}\right. $$ where $\mu$ and $\sigma$ are real parameters, dimension $n> ps$, with $s\in(0,1)$, $1
Keywords: Schroedinger-Hardy systems, existence of entire solutions, fractional p-Laplacian operator.
MSC: 35J47, 35B08, 35B09, 35R11; 35Q55, 35B33, 47G20
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