<b>Existence for an elliptic system with nonlinear boundary conditions</b> - doi: 10.5269/bspm.v28i2.11313

DOI: https://doi.org/10.5269/bspm.v28i2.11313

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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