Multiple positive solutions for nonlinear periodic problems
The authors discuss the existence and the multiplicity of positive solutions to the following \(p\)-Laplacian periodic problem: \[ \begin{cases} -(| x'(t)|^{p-2}x'(t))'=f(t,x(t)), \quad 0<t<b,\\ x(0=x(b),\quad x'(0)=x'(b), \end{cases} \] where the nonlinearity \(f\) is a \((p-1)\)-Carathéodory function with super-linear growth at the space-origin. Using variational methods involving the Cerami condition, the authors prove the existence of at least two positive solutions. In the particular case of the semi-linear problem (\(p=2\)), the existence of three distinct positive solutions is obtained using Morse theory.
scientific article; zbMATH DE number 5817643
scientific article