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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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