Nonnegative solutions to a weighted indefinite elliptic Schrödinger equation
Abstract
Abstract In this paper, we consider the following weighted problem involving an indefinite nonlinearity: $$\begin{aligned} \left\{ \! \begin{array}{lllllll} -\operatorname {div}(g(x)\nabla u)\!=\!\lambda _{1}\beta (x)u\!+\!\mu f(x,u)\!+\!W(x)h(u)\!+\! \eta u^{2_s^*\!-\!1}\ \text {in} \ \Omega ,\\ u=0 \ \text {on} \ \partial \Omega ,\\ u(x)\ge 0 \ \text {in} \ \Omega . \end{array}\right. \quad (P_{\mu ,\eta }) \end{aligned}$$ - div ( g ( x ) ∇ u ) = λ 1 β ( x ) u + μ f ( x , u ) + W ( x ) h ( u ) + η u 2 s ∗ - 1 in Ω , u = 0 on ∂ Ω , u ( x ) ≥ 0 in Ω . ( P μ , η ) where
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Mathematical Inequalities and Applications
Publication details
- Journal / source
- Journal of Fixed Point Theory and Applications
- Volume
- 28
- Issue
- 2
- Publication date
- 3 March 2026
- Language
- EN