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Ground state solutions for quasilinear Schrödinger equations with variable potential and superlinear reaction. (English) Zbl 1460.35100

The authors consider a quasilinear Schrödinger equation of the form \[ -\Delta u+V(x)u-\frac{1}{2}\Delta \left(u^2\right)u=g(u),\quad x\in\mathbb{R}^N, \] where \(N \geq 3\), \(V\in C(\mathbb{R}^N,[0,\infty))\) and \(g\in C(\mathbb{R},\mathbb{R})\) is superlinear at infinity. Under very general assumptions on \(V\) and \(g\) and by using variational tools and some new analytic techniques, it is shown that the problem above admits a ground state solution, where a solution is called a ground state solution if its energy is minimal among all nontrivial solutions.

MSC:

35J20 Variational methods for second-order elliptic equations
35J60 Nonlinear elliptic equations
35Q55 NLS equations (nonlinear Schrödinger equations)
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