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Existence of weak solutions for some local and nonlocal \(p\)-Laplacian problem. (English) Zbl 1491.35246

Summary: We study the existence of weak solutions for some elliptic \(p\)-Laplacian problems in the case where \(p\) depends on the solution itself. We consider two situations, when \(p\) is a local and nonlocal quantity. The main aim of this paper is to extend the results established by M. Chipot and H. B. de Oliveira [Math. Ann. 375, No. 1–2, 283–306 (2019; Zbl 1430.35106); correction ibid. 375, No. 1–2, 307–313 (2019)].

MSC:

35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J25 Boundary value problems for second-order elliptic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence

Citations:

Zbl 1430.35106
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References:

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