Multiple solutions for a class of the elliptic systems with square growth nonlinearity

초록

We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method for the dimension of the system which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory on the reduced finite dimensional subspace. 2010 Mathematics Subject Classification: 35J50, 35J55 Key Words and Phrases: elliptic system, reduction method, $(P.S.)$ condition, critical point theory, variational method