Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80886220170219On the existence of solutions to a class of semilinear Schrödinger equationsOn the existence of solutions to a class of semilinear Schrödinger equations75911299710.22055/jamm.2017.12997FAYaghoobJalilianDepartment of Mathematics, Razi University, Kermanshah, IranIrajDehsariDepartment of Mathematics, Razi University, Kermanshah, IranJournal Article20170619In this paper, we investigate the existence of a nontrivial weak solution for a class of quasilinear Schrödinger equations in the Sobolev space . First, we use a change of variables to obtain a well defined energy functional on . Then we find a manifold which is a natural constraint, and we prove that the restriction of the energy functional to this manifold attains its infimum. Finally, we show that this infimum point is a nontrivial weak solution for the equation.In this paper, we investigate the existence of a nontrivial weak solution for a class of quasilinear Schrödinger equations in the Sobolev space . First, we use a change of variables to obtain a well defined energy functional on . Then we find a manifold which is a natural constraint, and we prove that the restriction of the energy functional to this manifold attains its infimum. Finally, we show that this infimum point is a nontrivial weak solution for the equation.https://jamm.scu.ac.ir/article_12997_d4ab42cd3fe23af00e7154d1808d72d0.pdf