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On non-local nonlinear elliptic equations involving an eigenvalue problem

Authors
  • Chen, Ching-yu1
  • Kuo, Yueh-cheng1
  • Wang, Kuan-Hsiang1
  • Wu, Tsung-fang1
  • 1 National University of Kaohsiung, Kaohsiung, 811, Taiwan , Kaohsiung (Taiwan)
Type
Published Article
Journal
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Publisher
Springer International Publishing
Publication Date
Nov 29, 2021
Volume
116
Issue
1
Identifiers
DOI: 10.1007/s13398-021-01190-5
Source
Springer Nature
Keywords
Disciplines
  • Original Paper
License
Yellow

Abstract

The existence and multiplicity of solutions for a class of non-local elliptic boundary value problems with superlinear source functions are investigated in this paper. Using variational methods, we examine the changes arise in the solution behaviors as a result of the non-local effect. Comparisons are made of the results here with those of the elliptic boundary value problem in the absence of the non-local term under the same prescribed conditions to highlight this effect of non-locality on the solution behaviors. Our results here demonstrate that the complexity of the solution structures is significantly increased in the presence of the non-local effect with the possibility ranging from no permissible positive solution to three positive solutions and, contrary to those obtained in the absence of the non-local term, the solution profiles also vary depending on the superlinearity of the source functions.

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