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Bounded resonant problems driven by fractional Laplacian. (English) Zbl 1476.35300

Summary: In this paper we study the existence of nontrivial solutions for the fractional Laplacian resonance problem with a bounded nonlinearity via Morse theory and a penalization technique.

MSC:

35R11 Fractional partial differential equations
35A15 Variational methods applied to PDEs
35A16 Topological and monotonicity methods applied to PDEs
35J25 Boundary value problems for second-order elliptic equations
35J61 Semilinear elliptic equations
35R09 Integro-partial differential equations
45K05 Integro-partial differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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