Large and small solutions of a class of quasilinear elliptic eigenvalue problems
The authors deal with the existence of positive solutions of the quasilinear eigenvalue problem \[ \begin{cases} -\Delta_p u=\lambda f(u)\quad & \text{in }\Omega,\\ u=0\quad & \text{on }\partial \Omega,\end{cases} \tag{1} \] where \(1<p< \infty\), \(\lambda>0\). Under some suitable assumptions on \(f\), the authors obtain existence and uniqueness results for large positive solutions for (1). To this end they use mountain pass arguments and show that this solution develops to a spike layer solution.
scientific article; zbMATH DE number 1797533
scientific article