Existence results for quasilinear elliptic systems in RN
Stavrakakis, N. M.
Southwest Texas State University, Department of Mathematics
We prove existence results for the quasilinear elliptic system -∆pu = λα(x)|u|γ-2u + λb(x)|u|α-1|v|β+1u, -∆qv = 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 α, b, and d may change sign. For the unperturbed system (α = 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) = 0.
p-Laplacian, Nonlinear eigenvalue problems, Homogeneous Sobolev spaces, Maximum principle, Palais-Smale Condition
Stavrakakis, N. M., & Zographopoulos, N. B. (1999). Existence results for quasilinear elliptic systems in RN. <i>Electronic Journal of Differential Equations, 1999</i>(39), pp. 1-15.