Existence of solutions for a biharmonic equation with gradient term

Abstract

"In this paper, we mainly study the existence of radial solutions for a class of biharmonic equation with a convection term, involving two real parameters λ and ρ. We mainly use a combination of the fixed-point index theory and the Banach contraction theorem to prove that there are λ0 > 0 and ρ0 > 0 such the equation admits at least one radial solution for all (λ, ρ) ∈ [−λ0, ∞[ × [0, ρ0]. Keywords: Radial solution, biharmonic equation, index theory, existence."