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Mohsen Alimohammady

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
Faculty: Faculty of Mathematical Sciences
Address:
Phone: 011-35302462

Research

Title
Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket
Type
JournalPaper
Keywords
gradient-type systems, Sierpiński gasket, nonlinear elliptic equation, Palais-Smale condition
Year
2019
Journal Hacettepe Journal of Mathematics and Statistics
DOI
Researchers Haiffa Mohsen Buite ، Ghasem Alizadeh Afrouzi ، Mohsen Alimohammady

Abstract

In this paper, we establish the existence and multiplicity results of solutions for parametric quasi-linear systems of the gradient-type on the Sierpiński gasket is proved. Our technical approach is based on variational methods and critical points theory and on certain analytic and geometrical properties of the Sierpiński fractal. Indeed, using a consequence of the local minimum theorem due to Bonanno, the Palais-Smale condition cut off upper at r, and the Palais-Smale condition for the Euler functional we investigate the existence of one and two solutions for our problem under algebraic conditions on the nonlinear part. Moreover by applying a different three critical point theorem due to Bonanno and Marano we guarantee the existence of third solution for our problem.(400)