Electron. J. Diff. Equ., Vol. 2013 (2013), No. 102, pp. 1-25.

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

Michail V. Voitovich

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.

Show me the PDF file (350 KB), TEX file, and other files for this article.

Michail V. Voitovich
Institute of Applied Mathematics and Mechanics
Rosa Luxemburg Str. 74, 83114 Donetsk, Ukraine
email: voytovich@bk.ru

Return to the EJDE web page