Multiple positive solutions for biharmonic equation of Kirchhoff type involving concave-convex nonlinearities
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Date
2020-05-19
Authors
Meng, Fengjuan
Zhang, Fubao
Zhang, Yuanyuan
Journal Title
Journal ISSN
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