Sun, Yijing; Wu, Shaoping On a nonlinear elliptic equation with sublinear term at the origin. (Chinese. English summary) Zbl 0967.35053 Acta Math. Sci. (Chin. Ed.) 20, No. 4, 461-467 (2000). Summary: This paper deals with a class of semilinear elliptic Dirichlet boundary value problems \[ -\Delta u= g(x)|u|^{q-2} u+\lambda|u|^{p-2}u+ f(x),\quad x\in\Omega,\quad u|_{\partial\Omega}= 0 \] with a sign-changing or negative coefficient function for concave nonlinearities of the form \(|u|^{q-2} u\), \(1< q< 2\), and establishes some existence and multiplicity results. Cited in 2 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35J25 Boundary value problems for second-order elliptic equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:sign-changing function; sublinear terms; superlinear terms; barrier method; variational method PDFBibTeX XMLCite \textit{Y. Sun} and \textit{S. Wu}, Acta Math. Sci. (Chin. Ed.) 20, No. 4, 461--467 (2000; Zbl 0967.35053)