On the existence and regularity of vector solutions for quasilinear systems with linear coupling

摘要

We study the following coupled system of quasilinear equations:({-△pu + |u|p-2u =f(u) + λv,x ∈ RN,-△pv + |v|p-2v =g(v) + λu,x ∈ RN.)Under some assumptions on the nonlinear terms f and g,we establish some results about the existence and regularity of vector solutions for the p-Laplacian systems by using variational methods.In particular,we get two pairs of nontrivial solutions.We also study the different asymptotic behavior of solutions as the coupling parameter λ tends to zero.

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