Ground state solutions for the modified nonlinear Schrödinger equation with critical nonlinearities
DOI:
https://doi.org/10.12775/TMNA.2025.069Keywords
Modified nonlinear Schrödinger equation, ground state solution, variational method, Sobolev critical exponentAbstract
This paper is devoted to the study of the modified nonlinear Schrödinger equation which appears in various fields of physics. Our aim is to prove the existence of a ground state solution when the nonlinear term has a critical growth. By using a change of variables and performing a detailed energy estimate, we can obtain the existence of a ground state solution for general nonlinearities. Especially we are able to remove the 4-superlinear assumption, which extends previous known results.References
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