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《Nonlinear Analysis: Theory, Methods & Applications》2003,52(5):1535-1552
In this paper we use an algebraic topological argument due to Bahri and Coron to show how the topology of the domain influences the existence of positive solutions of the following problem involving the bilaplacian operator with the critical Sobolev exponentwhere is a bounded domain of with a smooth boundary . 相似文献
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Attila Pethö 《Journal of Number Theory》1980,12(3):334-338
In this paper I prove the following Theorem: Let α be a quadratic irrational number and let ? > 0, . Then there exists an effectively computable, positive constant c depending on α and ? such that has no solutions in natural numbers q. 相似文献
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M.Francesca Betta Anna Mercaldo François Murat M.Michaela Porzio 《Comptes Rendus Mathematique》2002,334(9):757-762
In this Note we consider a class of noncoercive nonlinear problems whose prototype is where is a bounded open subset of (N?2), △p is the so called p-Laplace operator (1<p<N) or a variant of it, μ is a Radon measure with bounded variation on or a function in , λ?0 and b belongs to the Lorentz space or to the Lebesgue space . We prove existence and uniqueness of renormalized solutions. To cite this article: M.F. Betta et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 757–762. 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2003,54(1):9-37
In this paper, we study the problemin the setting of the weighted sobolev space . The main novelty of our work is L∞ estimates on the solutions, and the existence of a weak and renormalized solution. 相似文献
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