Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 102, pp. 125.
Existence of bounded solutions for nonlinear fourthorder elliptic
equations with strengthened coercivity and lowerorder terms
with natural growth
Michail V. Voitovich
Abstract:
In this article, we consider nonlinear elliptic
fourthorder equations with the principal part satisfying a
strengthened coercivity condition, and a lowerorder 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 lowerorder 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;
lowerorder term; natural growth; Dirichlet problem;
bounded solution; Linfinityestimate.
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Michail V. Voitovich
Institute of Applied Mathematics and Mechanics
Rosa Luxemburg Str. 74, 83114 Donetsk, Ukraine
email: voytovich@bk.ru

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