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Eigenvalue problems of quasilinear elliptic systems on Rn.

Gong Bao Li (1987)

Revista Matemática Iberoamericana

In this paper we get the existence results of the nontrivial weak solution (λ,u) of the following eigenvalue problem of quasilinear elliptic systems-Dα (aαβ(x,u) Dβui) + 1/2 Dui aαβ(x,u)Dαuj Dβuj + h(x) ui = λ|u|p-2ui,   for x ∈ Rn, 1 ≤ i ≤ N and u = (u1, u2, ..., uN) ∈ E = {v = (v1, v2, ..., vN) | vi ∈ H1(Rn), 1 ≤ i ≤ N},where aαβ(x,u) satisfy the natural growth conditions. It seems that this kind of problem has never been dealt with before.

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