Multiplicity Results of Solutions to the Double Phase Problems of Schr?dinger-Kirchhoff Type with Concave-Convex Nonlinearities

The present paper is devoted to establishing several existence results for infinitely many solutions to Schrodinger-Kirchhoff-type double phase problems with concave-convex nonlinearities. The first aim is to demonstrate the existence of a sequence of infinitely many large-energy solutions by applying the fountain theorem as the main tool. The second aim is to obtain that our problem admits a sequence of infinitely many small-energy solutions. To obtain these results, we utilize the dual fountain theorem. In addition, we prove the existence of a sequence of infinitely many weak solutions converging to 0 in L infinity-space. To derive this result, we exploit the dual fountain theorem and the modified functional method.