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Fractional Kirchhoff-Choquard equation involving Schrödinger term and upper critical exponent. (English) Zbl 1480.35229

Summary: In this paper, we consider fractional degenerate and non-degenerate Kirchhoff type Schrödinger-Choquard problems with upper critical exponent, respectively. By studying the solutions of limit problems for above problems and establishing some local and global compactness results, we provide some sufficient conditions under which above problems have at least one or two bounded state solutions. Our main tools adopted in our proof are splitting theorem and linking theorem.

MSC:

35J62 Quasilinear elliptic equations
35R11 Fractional partial differential equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35J20 Variational methods for second-order elliptic equations
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