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Ground state solutions for Bessel fractional equations with irregular nonlinearities. (English) Zbl 1403.35281

Summary: We consider the semilinear fractional equation \[ (I-\Delta)^s u=a(x)|u|^{p-2}u\,\,\text{in}\,\,\mathbb R^N, \] where \(N\geq 3\), \(0<s<1\), \(2<p<2N/(N-2s)\) and \(a\) is a bounded weight function. Without assuming that \(a\) has an asymptotic profile at infinity, we prove the existence of a ground state solution.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35S05 Pseudodifferential operators as generalizations of partial differential operators
35J61 Semilinear elliptic equations
35R11 Fractional partial differential equations
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