Yujuan Chen

Boundary blow-up solutions for p-Laplacian elliptic equations of logistic type

We establish the existence, uniqueness and blow-up rate near the boundary of boundary blow-up solutions to p -Laplacian elliptic equations of logistic type −Δ p u = a(x)h(u) − b(x)f(u) , where Δ p u = div (|∇ u | p −2 ∇ u ) with p > 1, h(u)/u p −1 is non-increasing and f(u) is a function whose variation at infinity may be regular or rapid. In particular, our result regarding the blow-up rate reveals the main difference between regular variation function f and rapid variation function f .

Boundary blow-up solutions for elliptic equations with gradient terms and singular weights: existence, asymptotic behaviour and uniqueness

This paper deals with the non-negative boundary blow-up solutions of the equation Delta u = b(x)u(P) + c(s)u(sigma) vertical bar del u vertical bar(q) in Omega subset of R(N), where b(x), c(x) is an element of C(gamma) (Omega, R(+)) for some 0 < gamma < 1 and can be vanishing or singular on the boundary, and p, and q are non-negative constants. The existence and asymptotic behaviour of such a solution near the boundary are investigated, and we show how the nonlinear gradient term affects the results. As a consequence of the asymptotic behaviour, we also show the uniqueness result.