Sublinear singular elliptic problems with two parameters. (English) Zbl 1039.35042

Let \(\Omega\) be a smooth bounded domain in \(\mathbb R^N\) \((N\geq 2)\). The authors study the existence or nonexistence of solutions to the following boundary value problem \[ \begin{cases} -\Delta u+ K(x)g(u)=\lambda f(x,u)+\mu h(x)\quad &\text{in }\Omega,\\ u> 0\quad &\text{in }\Omega,\\ u=0\quad &\text{on }\partial\Omega,\end{cases}\tag{P\(_{\lambda,\mu}\)} \] where \(\lambda\) and \(\mu\) are positive parameters. Under suitable assumptions on \(K\), \(g\), \(f\) and \(h\) the authors using the maximum principle for elliptic equations establish several existence and nonexistence results for \((\text{P}_{\lambda,\mu})\).


35J65 Nonlinear boundary value problems for linear elliptic equations
35B50 Maximum principles in context of PDEs
58J55 Bifurcation theory for PDEs on manifolds
35J60 Nonlinear elliptic equations
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