Existence and quantum calculus of weak solutions for a class of two-dimensional Schrödinger equations in C+ $\mathbb{C}_{+}$

Abstract The aim of this paper is to investigate the existence of weak solutions for a two-dimensional Schrödinger equation with a singular potential in C+ $\mathbb{C}_{+}$. Under appropriate assumptions on the nonlinearity, we introduce a new type of quantum calculus via the Morse theory and variational methods. By applying Schrödinger type inequalities and the well-known Banach fixed point theorem in conjunction with the technique of measures of weak noncompactness, the new and more accurate estimations for boundary behaviors of them are also deduced.

Abstract licence: CC BY-NC-ND

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