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The Existence of Ground State Solutions for Schrödinger-Kirchhoff Equations Involving the Potential without a Positive Lower Bound

DOI: 10.4236/jamp.2023.113053, PP. 790-803

Keywords: Schrödinger-Kirchhoff Equations, Critical Exponential Growth, Ground State Solution, Degenerate Potential

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Abstract:

In this paper, we study the following Schrödinger-Kirchhoff equation \"\" where V(x) ≥ 0 and vanishes on an open set of R2 and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.

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