On the existence of solutions to a class of semilinear Schrödinger equations

Document Type : Original Paper


Department of Mathematics, Razi University, Kermanshah, Iran


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.


Main Subjects

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