Existence of bounded solutions for nonlinear fourth-order elliptic equations with strengthened coercivity and lower-order terms with natural growth

Abstract

In this article, we consider nonlinear elliptic fourth-order equations with the principal part satisfying a strengthened coercivity condition, and a lower-order term having a "natural" growth with respect to the derivatives of the unknown function. We assume that there is an absorption term in the equation, but we do not assume that the lower-order term satisfies the sign condition with respect to unknown function. We prove the existence of bounded generalized solutions for the Dirichlet problem, and present some a priori estimates.

Keywords

• Nonlinear elliptic equations
• strengthened coercivity
• lower-order term
• natural growth
• Dirichlet problem
• bounded solution
• L-infinity-estimate