# A nonhomogeneous critical Kirchhoff-Schr\"odinger type equation in $\mathbb{R}^{4}$ involving vanishing potentials

@article{Albuquerque2019ANC, title={A nonhomogeneous critical Kirchhoff-Schr\"odinger type equation in \$\mathbb\{R\}^\{4\}\$ involving vanishing potentials}, author={Francisco S. B. Albuquerque and Marcelo Castanheira Ferreira}, journal={arXiv: Analysis of PDEs}, year={2019} }

In this paper we establish the existence of high energy weak solutions for a Kirchhoff-Schrodinger type problem in $\mathbb R^4$ 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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