Existence results for quasilinear elliptic systems in R N
Year: 1999
Type: article
Abstract: We prove existence results for the quasilinear elliptic system -Δpu = λa(x)|u|γ-2u + λb(x)|u|α-1|v|β+1u, - Δqv = λd(x)|v|δ-2v + λb(x)|u|α+1|v|β-1v, where γ and δ may reach the critical Sobolev exponents, and the coefficient functions a, b, and d may change sign. For the unperturbed system (a = 0, b = 0), we establish the existence and simplicity of a positive principal eigenvalue, under the assumption that u(x) > 0, v(x) > 0, and lim |x|→∞ u(x) = lim|x|→∞ u(x) = 0.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W159238494