Exact multiplicity results for a \(p\)-Laplacian problem with concave--convex--concave nonlinearities
The authors study the exact number of positive solutions to the two-point Dirichlet boundary value problem \[ -\biggl(\varphi_p \bigl(u'(x) \bigr) \biggr)'= \lambda f\bigl(u (x)\bigr),\;-1<x<1, \quad u(-1)= u(1)=0, \] where \(p>1\), \(\varphi_p(y) =|y|^{p-2} y\), \(f\in C^2(0,\infty)\) satisfies \(f(0)=0\) and has at least two distinct simple positive zeros \(b<c\) and \(f''\) changes sign more than twice on \((0,\infty)\). The main tool they used is the time-map method.
scientific article; zbMATH DE number 1901883
scientific article