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Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations. (English) Zbl 1359.35212

This article considers existence, multiplicity and asymptotic behavior of entire solutions for a series of stationary Kirchhoff fractional \(p\)-Laplacian equations. The results in this paper extend recent theorems in several directions. Moreover, weaker assumptions are required than the recent literature on stationary Kirchhoff fractional problems, for example, in the non-degenerate case, the authors replace the monotonicity assumption of the main Kirchhoff function \(M\) by a weaker condition.

MSC:

35R11 Fractional partial differential equations
35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35B09 Positive solutions to PDEs
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