New Positive Solutions of Nonlinear Elliptic PDEs

İNÇ M., Bouteraa N., AKINLAR M. A., Benaicha S., Chu Y., Weber G., ...More

APPLIED SCIENCES-BASEL, vol.10, no.14, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 14
  • Publication Date: 2020
  • Doi Number: 10.3390/app10144863
  • Journal Name: APPLIED SCIENCES-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Agricultural & Environmental Science Database, Applied Science & Technology Source, Communication Abstracts, INSPEC, Metadex, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: positive (global) solution, (strict) upper and lower solutions, multiplicity of positive solutions, elliptic BVPs, BOUNDARY-VALUE-PROBLEMS, ASYMPTOTIC-BEHAVIOR, KIRCHHOFF-TYPE, EXISTENCE, EQUATIONS
  • Middle East Technical University Affiliated: No

Abstract

We are concerned with positive solutions of two types of nonlinear elliptic boundary value problems (BVPs). We present conditions for existence, uniqueness and multiple positive solutions of a first type of elliptic BVPs. For a second type of elliptic BVPs, we obtain conditions for existence and uniqueness of positive global solutions. We employ mathematical tools including strictly upper (SU) and strictly lower (SL) solutions, iterative sequence method and Amann theorem. We present our research findings in new original theorems. Finally, we summarize and indicate areas of future study and possible applications of the research work.