Existence and asymptotic behavior of ground states for quasilinear singular equations involving Hardy–Sobolev exponents
- Alves, C.O.
- Goncalves, J.V.
- Santos, C.A.
DOIAbstract
AbstractWe study the existence and decaying rate of solutions for the quasilinear problem{−Δpu=ρ(x)f(u)+λ|x|θg(u)inRN,u>0inRN,u(x)0, where Δp stands for the p-Laplacian operator, 1<p<N, ρ:RN→[0,∞) is continuous and not identically zero, λ⩾0 is a parameter, |x| is the Euclidean norm of x, 0⩽θ⩽p, f,g:[0,∞)→[0,∞) are continuous and nondecreasing, f has sublinear growth and the Hardy–Sobolev exponent pθ∗:=p(N−θ)/(N−p) bounds the growth of g. We deal with variational methods and the lower and upper solutions technique
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