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.
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| Michail V. Voitovich |
Institute of Applied Mathematics and Mechanics
Rosa Luxemburg Str. 74, 83114 Donetsk, Ukraine
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