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Qualitative properties of anisotropic elliptic Schrödinger equations
Afrouzi, Ghasem A. ; Mirzapour, Maryam ; Rǎdulescu, Vicenţiu, 1958-
We consider a class of nonlinear stationary Schrödinger-type equations and we are concerned with sufficient properties that guarantee the existence of multiple solutions in a suitable Sobolev space ...with variable exponents. We first establish that in the case of small perturbations, the problem admits at least two weak solutions. Next, in the case of convex-concave nonlinearities, we obtain conditions for the existence of infinitely many solutions with high (resp., small) energies. The arguments combine variational techniques with a careful analysis of the energy levels.
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