Displaying similar documents to “Limit behaviour of singular solutions of some semilinear elliptic equations”

Converse problem for the two-component radial Gross-Pitaevskii system with a large coupling parameter

Casteras, Jean-Baptiste, Sourdis, Christos

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We consider strongly coupled competitive elliptic systems that arise in the study of two-component Bose-Einstein condensates. As the coupling parameter tends to infinity, solutions that remain uniformly bounded are known to converge to a segregated limiting profile, with the difference of its components satisfying a limit scalar PDE. In the case of radial symmetry, under natural non-degeneracy assumptions on a solution of the limit problem, we establish by a perturbation argument its...

Multilevel correction adaptive finite element method for semilinear elliptic equation

Qun Lin, Hehu Xie, Fei Xu (2015)

Applications of Mathematics

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A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence, solving the semilinear elliptic problem can reach almost the same efficiency as the adaptive method for the associated...

Multiplicity of solutions for a singular p-laplacian elliptic equation

Wen-shu Zhou, Xiao-dan Wei (2010)

Annales Polonici Mathematici

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The existence of two continuous solutions for a nonlinear singular elliptic equation with natural growth in the gradient is proved for the Dirichlet problem in the unit ball centered at the origin. The first continuous solution is positive and maximal; it is obtained via the regularization method. The second continuous solution is zero at the origin, and follows by considering the corresponding radial ODE and by sub-sup solutions method.