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In this paper, we study the existence of infinitely many nontrivial solutions for the following semilinear Schrödinger equation: { − Δ u + V (x) u = f (x , u) , x ∈ R N , u ∈ H 1 (R N) , where the potential V is continuous and is allowed to be sign-changing. By using a variant fountain theorem, we obtain the existence of infinitely many high energy solutions under the condition that the nonlinearity f (x , u) is of super-linear growth at infinity. The super-quadratic growth condition imposed on F (x , u) = ∫ 0 u f (x , t) d t is weaker than the Ambrosetti–Rabinowitz type condition and the similar conditions employed in the references. [ABSTRACT FROM AUTHOR]

In this paper, we apply the method associated with the technique of measure of noncompactness and the Darbo fixed point theorem to study the existence of solutions of the Darboux problem involving the distributional Henstock-Kurzweil integral. Meanwhile, an example is provided to illustrate our results. [ABSTRACT FROM AUTHOR]