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February, 2021 Existence of Positive Solution to Schrödinger-type Semipositone Problems with Mixed Nonlinear Boundary Conditions
Eunkyung Ko, Eun Kyoung Lee, Inbo Sim
Taiwanese J. Math. 25(1): 107-124 (February, 2021). DOI: 10.11650/tjm/200702

Abstract

We studied the existence of a positive solution to Schrödinger-type semipositone problems with mixed nonlinear boundary conditions. By considering the cases when the reaction term with a parameter satisfies a superlinear and a sublinear growth condition at infinity, we established the existence of a positive solution for the large and small values of the parameter, respectively. The proofs are mainly based on the sub- and supersolution method for the sublinear case and the mountain pass lemma with $C^{1,\alpha}(\overline{\Omega})$-regularity for the superlinear case.

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Eunkyung Ko. Eun Kyoung Lee. Inbo Sim. "Existence of Positive Solution to Schrödinger-type Semipositone Problems with Mixed Nonlinear Boundary Conditions." Taiwanese J. Math. 25 (1) 107 - 124, February, 2021. https://doi.org/10.11650/tjm/200702

Information

Received: 9 April 2020; Revised: 23 June 2020; Accepted: 26 July 2020; Published: February, 2021
First available in Project Euclid: 5 August 2020

Digital Object Identifier: 10.11650/tjm/200702

Subjects:
Primary: 35J20, 35J66

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 1 • February, 2021
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