Multiplicity Results for a Second-Order Boundary-Value Problems With Variable Expnents

Subject Areas : Statistics

ghasem Alizadeh Afroozi ¹ , Mostafa Negravi ² , Mehdi Azhini ³

1 - Department of Mathematics, Faculty of Mathematical Sciences, Mazandaran University, Babolsar, Iran
2 - Department of Mathematics and Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Mathematics and Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received: 2019-04-08 Accepted : 2019-11-03 Published : 2020-12-21

Keywords: نظریه نقاط بحرانی, p(x)- لاپلاسین, شرایط نویمن, جواب های چندگانه,

Abstract :

In this paper, we introduce the Lebesgue -Sobolev spaces critical points theory then we consider the boundary value problem involving an ordinary differential equation with p(x)-Laplacian operator, and nonhomogeneous Neumann conditions. Existence results for ordinary differential equations with elliptic Neumann problems that depending on two real parameters are investigated. Precisely, by using the critical point theory, we show the existence of three weak solutions for p(x)-Laplacian problems. Using the critical point theorems we have proved, we give some conclusionsIn this paper, we introduce the Lebesgue -Sobolev spaces critical points theory then we consider the boundary value problem involving an ordinary differential equation with p(x)-Laplacian operator, and nonhomogeneous Neumann conditions. Existence results for ordinary differential equations with elliptic Neumann problems that depending on two real parameters are investigated. Precisely, by using the critical point theory, we show the existence of three weak solutions for p(x)-Laplacian problems. Using the critical point theorems we have proved, we give some conclusions

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