Multiple positive solutions for biharmonic equation of Kirchhoff type involving concave-convex nonlinearities

Date

2020-05-19

Authors

Meng, Fengjuan
Zhang, Fubao
Zhang, Yuanyuan

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we study the multiplicity of positive solutions for the biharmonic equation of Kirchhoff type involving concave-convex nonlinearities, ∆2u - (α + b ∫ℝN |∇u|2dx) ∆u + V(x)u = λƒ1(x)|u|q-2 u + ƒ2(x)|u|p-2u. Using the Nehari manifold, Ekeland variational principle, and the theory of Lagrange multipliers, we prove that there are at least two positive solutions, one of which is a positive ground state solution.

Description

Keywords

Biharmonic equation, Ground state solution, Nehari manifold, Concave-convex nonlinearity

Citation

Meng, F., Zhang, F., & Zhang, Y. (2020). Multiple positive solutions for biharmonic equation of Kirchhoff type involving concave-convex nonlinearities. <i>Electronic Journal of Differential Equations, 2020</i>(44), pp. 1-15.

Rights

Attribution 4.0 International

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