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Nehari manifold for weighted singular fractional \(p\)-Laplace equations. (English) Zbl 1512.34052

In this paper, the authors consider weighted singular fractional \(p\)-Laplacian problems involving a bounded weight function. Firstly, some auxiliary results about the \(\psi\)-Riemann-Liouville fractional integral and \(\psi\)-Hilfer fractional derivatives are given. Based on the the technique of the Nehari manifold, the existence of two positive solutions for the addressed problems is presented. At the same time, some related propositions and theorems are obtained.

MSC:

34B16 Singular nonlinear boundary value problems for ordinary differential equations
34A08 Fractional ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
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