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On a nonlinear elliptic equation with sublinear term at the origin. (Chinese. English summary) Zbl 0967.35053

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.

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)
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