منابع مشابه
Nodal Domains for the p-Laplacian
In this paper we consider the eigenvalue problem − pu = λ(m)|u|p−2u, u ∈ W 1,p 0 ( ) where p > 1, p is the p-Laplacian operator, λ > 0, is a bounded domain in R(N ≥ 1) and m is a given positive function in L( ) (r depending on p and N ). We prove that the second positive eigenvalue admits exactly two nodal domains. AMS subject classification: 35J20, 35J70, 35P05, 35P30.
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Dynamics of planar domains with multiply connected moving boundaries driven by the gradient of a scalar field that satisfies an elliptic PDE is studied. We consider the question: For which kind of PDEs the domains are algebraic, provided the field has singularities at a finite number of fixed points? The construction reveals a direct connection with the theory of the Calogero-Moser systems rela...
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This work is devoted to study the existence of solutions to equations of the p-Laplacian type in unbounded domains. We prove the existence of at least one solution, and under further assumptions, the existence of in nitely many solutions. We apply the mountain pass theorem in weighted Sobolev spaces.
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In the paper the differential inequality ∆pu +B(x, u) 6 0, where ∆pu = div(‖∇u‖ ∇u), p > 1, B(x, u) ∈ C( n × , ) is studied. Sufficient conditions on the function B(x, u) are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool.
متن کاملTopology of Quadrature Domains
Formulas like (0.1) and (0.2) are called quadrature identities, and the corresponding domains of integration are called (classical) quadrature domains. Various classes of quadrature domains have been known for quite some time, see e.g. Neumann’s papers [39, 40] from the beginning of the last century, but the systematic study began only with the work of Davis [13], and Aharonov and Shapiro [2]. ...
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ژورنال
عنوان ژورنال: Complex Analysis and Operator Theory
سال: 2008
ISSN: 1661-8254,1661-8262
DOI: 10.1007/s11785-008-0103-9