Existence for an elliptic system with nonlinear boundary conditions - doi: 10.5269/bspm.v28i2.11313
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https://doi.org/10.5269/bspm.v28i2.11313Palabras clave:
Steklov problems, weights, elliptic systems, nonlinear boundary conditions.Resumen
In this paper we prove the existence of a weak solution to the following system
Delta_p u = Delta_q v = 0 in Omega
|nabla u|^{p-2}partial_{nu}u = f(x,u) - (alpha+1)K(x) |u|^{alpha-1}u |v|^{beta+1} + f_1 on partial Omega
|nabla v|^{q-2}partial_{nu}v = g(x,u) - (beta+1)K(x) |v|^{beta-1}v |u|^{alpha+1}+ g_1 on partial Omega
where Omega is a bounded domain in R^N (N ≥ 2), f_1, g_1, f, g and K are functions that satisfy some conditions.
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