Strongly indefinite problems with exponential growth in the plane - Menezes, Marta Nascimento (2024)
In this work, we study questions related to the existence of ground state and nontrivial solution for some classes of strongly inde nite problems with exponential growth in the plane. Firstly, we study Hamiltonian systems, which have been widely addressed in the last years in the mathematical study of standing wave solutions in nonlinear optics. Secondly, we deal with a class of periodic Schrödinger equations involving exponential critical growth, in which we do not use the classic Ambrosetti-Rabinowitz condition. In order to obtain our results, we use variational methods, namely, a reduction method and linking theorems.