Positive Solutions of Indefinite Semipositone Elliptic Problems

Ruyun Ma ^[1] ; Yali Zhang ^[1] ; Yan Zhu ^[1]
1. [1] Northwest Normal University
  
  Northwest Normal University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
Idioma: inglés
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Resumen
- 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.