A nonhomogeneous critical Kirchhoff-Schrödinger type equation in ℝ⁴ involving vanishing potentials

2019/09/11 by Francisco S. B. Albuquerque, Francisco S. Albuquerque, Albuquerque, Francisco S. +2
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1909.05080

Updated version. Submitted paper

arxiv created 2020/06/18 · arxiv updated 2020/06/22

Abstract

In this paper we establish the existence of mountain pass and negative energy weak solutions for a Kirchhoff-Schrödinger type problem in \mathbb R⁴ involving a critical nonlinearity and a suitable small perturbation. The arisen competition between the terms due to the nonlocal coefficient and critical nonlinearity turns out to be rather interesting. The main tools used in the present work are variational methods and the Lions' Concentration Compactness Principle.

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