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Positive solutions for nonlinear Schrödinger-Kirchhoff equations in \(\mathbb{R}^3\). (English) Zbl 1437.35287
Summary: In this paper, we study the nonlinear Schrödinger-Kirchhoff-type equation with pure power nonlinearities in \(\mathbb{R}^3\) by variational methods. By carrying out the constrained minimization on a special manifold which is a combination of the Nehari manifold and Pohozaev manifold, we proved the existence of positive radial solutions of this equation for the power \(p \in (1, 5)\). The results of this paper extend some existing conclusions, especially for \(p \in (1, 2]\).
MSC:
35J60 Nonlinear elliptic equations
35B09 Positive solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A15 Variational methods applied to PDEs
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