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