Existence of bounded solutions for nonlinear fourth-order elliptic equations with strengthened coercivity and lower-order terms with natural growth
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...
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| Format: | Article |
| Language: | English |
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Texas State University
2013-04-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/102/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |