Large solutions to an anisotropic quasilinear elliptic problem |
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| Authors: | Jorge García-Melián Julio D Rossi José C Sabina de Lis |
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| Institution: | 1. Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271, La Laguna, Spain
3. Instituto Universitario de Estudios Avanzados (IUdEA) en Física Atomica, Molecular y Fotonica, Facultad de Física, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38203, La Laguna, Spain
2. Departamento de Matemática, FCEyN UBA, Universidad de Buenos Aires, Pab 1, (1428), Buenos Aires, Argentina
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| Abstract: | In this paper we consider existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem ${\rm div}_x (|\nabla_x u|^{p-2}\nabla_xu)(x,y) + {\rm div}_y (|\nabla_y u|^{q-2}\nabla_y u) (x, y) = u^r(x, y)$ in a bounded domain ${\Omega \subset \mathbb{R}^N \times \mathbb{R}^M}In this paper we consider existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem
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divx (|?x u|p-2?xu)(x,y) + divy (|?y u|q-2?y u) (x, y) = ur(x, y){\rm div}_x (|\nabla_x u|^{p-2}\nabla_xu)(x,y) + {\rm div}_y (|\nabla_y u|^{q-2}\nabla_y u) (x, y) = u^r(x, y) |
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