Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 102, pp. 1-25.
Title: Existence of bounded solutions for nonlinear fourth-order elliptic
equations with strengthened coercivity and lower-order terms
with natural growth
Author: Michail V. Voitovich (Inst. of Applied Math. and Mechanics, Donetsk, Ukraine)
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.
Submitted April 5, 2013. Published April 24, 2013.
Math Subject Classifications: 35B45, 35B65, 35J40, 35J62.
Key Words: Nonlinear elliptic equations; strengthened coercivity;
lower-order term; natural growth; Dirichlet problem;
bounded solution; L-infinity-estimate.