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On the fractional \(p\)-Laplacian problems. (English) Zbl 1504.35615

Summary: This paper deals with nonlocal fractional \(p\)-Laplacian problems with difference. We get a theorem which shows existence of a sequence of weak solutions for a family of nonlocal fractional \(p\)-Laplacian problems with difference. We first show that there exists a sequence of weak solutions for these problems on the finite-dimensional subspace. We next show that there exists a limit sequence of a sequence of weak solutions for finite-dimensional problems, and this limit sequence is a sequence of the solutions of our problems. We get this result by the estimate of the energy functional and the compactness property of continuous embedding inclusions between some special spaces.

MSC:

35R11 Fractional partial differential equations
35K92 Quasilinear parabolic equations with \(p\)-Laplacian
26A33 Fractional derivatives and integrals
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