Existence of solutions for a p-Laplacian system with a nonresonance condition between the first and the second eigenvalues
Abstract
In this article, we study the existence of positive solutions for the quasilinear elliptic system
−∆_p u(x) = f_1(x, v(x)) + h_1(x) in Ω,
−∆_p v(x) = f_2(x, u(x)) + h_2(x) in Ω,
u = v = 0 on ∂Ω,
where f_i(x, s), (i = 1, 2) locates between the first and the second eigenvalues of the p-Laplacian. To prove the existence of solutions, we use a topological method the Leray-Schauder degree.
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References
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