Existence for an elliptic system with nonlinear boundary conditions
In this paper we prove the existence of a weak solution to the following system△_p u = △_q v = 0 in Ω,|∇u|^{p−2} ∂_ν u = f(x,u) − (α + 1)K(x)|u|^{α−1}u|v|^{β+1} + f1 on ∂Ω,|∇v|^{q−2} ∂_ν v = g(x,v) − (β + 1)K(x)|v|^{β−1}v|u|^{α+1} + g1 on ∂Ω,where Ω is a bounded domain in RN (N ≥ 2), f1, g1, f, g an...
| Päätekijät: | , , , |
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| Aineistotyyppi: | Artikkeli |
| Kieli: | English |
| Julkaistu: |
Sociedade Brasileira de Matemática
2010-10-01
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| Sarja: | Boletim da Sociedade Paranaense de Matemática |
| Aiheet: | |
| Linkit: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/11313/6134 |
| Yhteenveto: | In this paper we prove the existence of a weak solution to the following system△_p u = △_q v = 0 in Ω,|∇u|^{p−2} ∂_ν u = f(x,u) − (α + 1)K(x)|u|^{α−1}u|v|^{β+1} + f1 on ∂Ω,|∇v|^{q−2} ∂_ν v = g(x,v) − (β + 1)K(x)|v|^{β−1}v|u|^{α+1} + g1 on ∂Ω,where Ω is a bounded domain in RN (N ≥ 2), f1, g1, f, g and K are functions that satisfy some conditions. |
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| ISSN: | 0037-8712 2175-1188 |