A class of modified nonlinear fourth-order elliptic equations with unbounded potential. Issue 5 (4th May 2021)

• Record Type: Journal Article
• Authors: Oliveira Junior, J. C.
• Is Part Of: Complex variables and elliptic equations. Volume 66:Issue 5(2021)
• Page Start: 876
• Page End: 891
• Publication Date: 2021-05-04
• Subjects: Fourth-order operator -- quasilinear equations -- Nehari manifold -- unbounded potential -- variational methods; 35J35 -- 35J62 -- 35Q35; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1751135
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : This paper is concerned on the fourth-order elliptic equation Δ 2 u − Δ u + V ( x ) u − λ Δ [ ρ ( u 2 ) ] ρ ′ ( u 2 ) u = f ( u ) in R N, u ∈ W 2, 2 ( R N ), P λ where Δ 2 = Δ ( Δ ) is the biharmonic operator, 3 ≤ N ≤ 6, the radially symmetric potential V may change sign and inf R N V ( x ) = − ∞ is allowed. If f satisfies a type of nonquadracity and monotonicity conditions and ρ is a suitable smooth function, we prove, via variational approach, the existence of a radially symmetric nontrivial ground state solution u λ for problem ( P λ ) for all λ ≥ 0 .