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 variat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-04-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-018-0975-1 |
| Summary: | 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. |
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| ISSN: | 1687-2770 |