Infinitely many solutions for a class of fractional equations via variant fountain theorems

Abdelilah Azghay; Mohammed  Massar; Abderrahim  El Mhouti

doi:10.5269/bspm.66418

Abdelilah Azghay ANLA, FSTH, Abdelmalek Essaadi University, Tetouan, Morocco https://orcid.org/0000-0003-1300-8805
Mohammed Massar ANLA, FSTH, Abdelmalek Essaadi University, Tetouan, Morocco
Abderrahim El Mhouti ISISA, Abdelmalek Essaadi University, Tetouan, Morocco

Resumo

This article is concerned with a class of fractional type equation involving an anisotropic operator and potential of the form $$(-\Delta_x)^s u-\Delta_yu+\Phi(x,y)u=g(x,y,u),\;(x,y)\in\mathbb{R}^n\times\mathbb{R}^m.$$ By means of the variational method and the variant fountain theorems, we investigate the existence of infinitely many high or small energy solutions without the usual assumption of coerciveness on the potential $\Phi$ in the different cases when the nonlinear term is either asymptotically linear or superquadratic growth.

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