Existence, multiplicity and stability results for positive solutions of nonlinear \(p\)-Laplacian equations
In the present study the authors are mainly interested in the positive solutions of the following boundary value problem of nonlinear \(p\)-Laplacian equations \[ -\Delta_pu=\lambda f(u),\text{ in }\Omega\quad u=0,\text{ on }\partial\Omega,\tag{1} \] where \(\lambda>0\), \(p>1\), \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) and \(f\) is a given nonnegative, nondecreasing function. The author studies both the existence of solution to (1) and extends part of the Crandall-Rabinowitz bifurcation theory to this problem. Moreover, the stability of solutions of the parabolic counterparts of (1) is investigated.
scientific article; zbMATH DE number 2109896