A fourth order elliptic problem of Kirchhoff type and finding infinitely many weak solution for it

Subject Areas : Statistics

Karimeh  Ardeshiri ¹ (Department of Mathematics, Mazandaran University, Mazandaran, Iran)
Somayeh  Khademloo ² (Department of Mathematics, Noshirvani University of Technology, Babol, Iran)
ghasem  alizadeh afrouzi ³ (Department of Mathematics, Mazandaran University, Mazandaran, Iran)

Received: 2019-07-17 Accepted : 2020-09-15 Published : 2021-07-23

Keywords: بی‌نهایت جواب ضعیف, نظریه‌ی نقطه‌ی بحرانی, پتانسیل چند تکینگی معکوس مربعی, کیرشهف مرتبه‌ی چهار, معادله‌ی بیضوی,

Abstract :

This paper is devoted to the existence of infinitely many solutions for a forth order elliptic Kirchhoff problem involving Multi-singular inverse square potentials in a bounded domain using the methods in nonlinear analysis, precisely the variational methods. Nonlinear analysis is a powerful tool for solving many physical models and a technique for proving the solvability of them.Among the methods can be considered in nonlinear analysis, variational methods can prove the existence and multiplicity of solutions without finding the exact value of them.Accordingly, we shall be told, perhaps, that we can find in this field of analysis one of the most applications of analysis in solving the real models of natural problems.The most important feature of the problem proposed in this article, is the existence of singular points in the domain. Using the critical point theory, we prove that there exists an interval in which, the problem has a sequence of distinct weak solutions.In other word, the existence of infinitely many solutions for this problem can be proved.This problem is of the type time independent Poison-Schrodinger equation appearing in an interesting physical context.

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