Resumen de Positive Solutions of Indefinite Semipositone Elliptic Problems

Ruyun Ma, Yali Zhang, Yan Zhu

• We are concerned with the parametrized family of problems Lu = λa(x)( f (u) − l), x ∈ , u = 0, x ∈ ∂, (P) whereis a bounded domain of RN (N ≥ 3) with regular boundary ∂, Lis a general second-order uniformly elliptic operator, λ, l > 0, a : → R is a continuous function which may change sign, f : R+ → R is subcritical and superlinear at infinity. Under some suitable conditions, we obtain there exists λ0 > 0 such that (P) has positive solutions for all 0 < λ ≤ λ0 by topological degree argument and a priori estimates.

  In doing so, we require f to be of regular variation at infinity.