Open AccessA class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$
Author(s) -
Zijian Wu,
Haibo Chen
Publication year - 2021
Publication title -
electronic journal on the qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2021.1.71
Subject(s) - nehari manifold , regular polygon , mathematics , multiplicity (mathematics) , class (philosophy) , order (exchange) , mathematical analysis , pure mathematics , nonlinear system , physics , geometry , computer science , finance , quantum mechanics , artificial intelligence , economics
In this article, we study the multiplicity of solutions for a class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$. Under the appropriate assumption, we prove that there are at least two solutions for the equation by Nehari manifold and Ekeland variational principle, one of which is the ground state solution.