• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.229-245
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• 2023

In this paper, we consider cooperative elliptic systems under conjugation conditions. We first prove the existence of the state for 2 × 2 cooperative elliptic systems with Dirichlet and Neumann conditions, then we find the set of equations and inequalities that characterizes the optimal control of distributed type for these systems. The case of n × n cooperative systems is also established.

• 대한수학회보
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• 제51권3호
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• pp.789-801
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• 2014

In this paper, we study the existence of ground state solutions for a class of non-resonant cooperative elliptic systems by a variant weak linking theorem. Here the classical Ambrosetti-Rabinowitz superquadratic condition is replaced by a general super quadratic condition.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.619-630
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• 2015

This paper is devoted to investigate the multiple solutions for a class of the cooperative elliptic system involving subcritical Sobolev exponents on the bounded domain with smooth boundary. We first show the uniqueness and the negativity of the solution for the linear system of the problem via the direct calculation. We next use the variational method and the mountain pass theorem in the critical point theory.