Article Contents

2020, Volume 40, Issue 4: 2165-2187. Doi: 10.3934/dcds.2020110

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Multiple positive solutions of saturable nonlinear Schrödinger equations with intensity functions

Tai-Chia Lin^1,2, and
Tsung-Fang Wu^3, ,

1.
Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan
2.
Mathematics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
3.
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan

^*Corresponding author: T. F. Wu
^*Corresponding author: T. F. Wu

Received: April 2019

Published: January 2020

T.C. Lin is partially supported by Center for Advanced Study in Theoretical Sciences (CASTS) and the Ministry of Science and Technology, Taiwan grant MOST-106-2115-M-002-003-MY3. T.F. Wu is partially supported by the Ministry of Science and Technology, Taiwan grant MOST-108-2115-M-390-007-MY2 and the National Center for Theoretical Sciences, Taiwan

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Abstract

In this paper, we study saturable nonlinear Schrödinger equations with nonzero intensity function which makes the nonlinearity become not superlinear near zero. Using the Nehari manifold and the Lusternik-Schnirelman category, we prove the existence of multiple positive solutions for saturable nonlinear Schrödinger equations with nonzero intensity function which satisfies suitable conditions. The ideas contained here might be useful to obtain multiple positive solutions of the other non-homogeneous nonlinear elliptic equations.

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Mathematics Subject Classification: Primary: 335J20, 35J60; Secondary: 35A15, 35B09.

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