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Existence of bound and ground states for a class of Kirchhoff‐Schrödinger equations involving critical Trudinger‐Moser growth
Author(s) -
Albuquerque José Carlos,
Araújo Yane Lísley,
Clemente Rodrigo
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5382
Subject(s) - mathematics , infinity , nonlinear system , class (philosophy) , domain (mathematical analysis) , compact space , mathematical analysis , sign (mathematics) , exponential growth , ground state , term (time) , exponential function , state (computer science) , physics , quantum mechanics , artificial intelligence , computer science , algorithm
In this paper, we discuss the existence of bound and ground state solutions for a class of fractional Kirchhoff equations defined on the whole real line. The equation involves a nonlinear term with critical exponential growth in the Trudinger‐Moser sense. We deal with periodic and asymptotically periodic potential, which may change sign. We handle with the lack of compactness because of the unboundedness of the domain and the critical behavior of the nonlinearity. The main theorems are stated without the well‐known Ambrosetti‐Rabinowitz condition at infinity.