Geodesic
Schrödinger equation with asymptotically linear nonlinearities
Filomat, Tome 36 (2022) no. 2, p. 629

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DOI

In this paper, we investigate a quasilinear Schrödinger problem under Dirichlet boundary condition in a regular domain with asymptotically linear nonlinearities. We use Cerami version of the mountain pass theorem to prove the existence of solution without using the Ambrosetti-Rabionovitz condition or any of its refinements. Then, we prove that the same techniques work when the nonlinearity is superlinear and subcritical at infinity
DOI : 10.2298/FIL2202629E
Classification : 35J05, 35J65, 35J20, 35J60, 35K57, 35J70
Keywords: Asymptotically linear, variational method, Schrödinger equations, Cerami sequence 
Amel El-Abed; Abir Amor Ben Ali; Makkia Dammak. Schrödinger equation with asymptotically linear nonlinearities. Filomat, Tome 36 (2022) no. 2, p. 629 . doi: 10.2298/FIL2202629E
@article{10_2298_FIL2202629E,
     author = {Amel El-Abed and Abir Amor Ben Ali and Makkia Dammak},
     title = {Schr\"odinger equation with asymptotically linear nonlinearities},
     journal = {Filomat},
     pages = {629 },
     year = {2022},
     volume = {36},
     number = {2},
     doi = {10.2298/FIL2202629E},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2202629E/}
}
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