Existence and multiplicity of solutions for the fractional Schrödinger equation with steep potential well and perturbation

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In the present paper, we investigate the solutions of a fractional Schrodinger equation with sublinear perturbation and steep potential well. First, we obtain the existence of at least one solution by the minimisation result due to Mawhin and Willem. Second, by virtue of the symmetric mountain pass theorem, the existence criteria of infinitely many solutions are established. Lastly, an example is given to demonstrate the main results.