Quasilinear Schrödinger equations with singular and vanishing potentials involving nonlinearities with critical exponential growth

2021 ◽  
pp. 1
Author(s):  
Yane Lísley Araújo ◽  
Gilson Carvalho ◽  
Rodrigo Clemente
Keyword(s):  
Exponential Growth ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Critical Exponential Growth ◽  
Vanishing Potentials

Hamiltonian systems of Schrödinger equations with vanishing potentials

2020 ◽  
pp. 2050074
Author(s):  
E. Toon ◽  
P. Ubilla
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Positive Solutions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Cerami Sequence ◽  
Cerami Sequences ◽  
Vanishing Potentials

In this paper, by means of minimax techniques involving Cerami sequences, we prove the existence of at least one pair of positive solutions for a Hamiltonian system of Schrödinger equations in [Formula: see text] with potentials vanishing at infinity and subcritical nonlinearities which are superlinear at the origin and at infinity. We establish new estimates to prove the boundedness of a Cerami sequence.

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