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 Solvability for a class of the systems of the nonlinear elliptic equations Bull. Korean Math. Soc. 2012 Vol. 49, No. 1, 1-10 https://doi.org/10.4134/BKMS.2012.49.1.1Published online January 1, 2012 Tacksun Jung and Q-Heung Choi Kunsan National University, Inha University Abstract : Let $\Omega$ be a bounded subset of $\mathbb R^n$ with smooth boundary. We investigate the solvability for a class of the system of the nonlinear elliptic equations with Dirichlet boundary condition. Using the mountain pass theorem we prove that the system has at least one nontrivial solution. Keywords : system of nonlinear elliptic equations, mountain pass theorem, $(P.S.)$ condition, critical point theory MSC numbers : 35J50, 35J55, 35J20, 35Q72 Full-Text :