Existence of positive and of multiple solutions for nonlinear periodic problems
The paper deals with the study of a scalar periodic problem of the following form: \[ -(| x'(t)| ^{p-2}x'(t))'\in \partial j(t,x(t))\quad\text{for a.a. }t\in T=[0,b], \] \[ x(0)=x(b),\quad x'(0)=x'(b), \] where \(\partial j(t,\cdot)\) denotes the generalized subdifferential, \(1<p<+\infty,\, j:T\times \mathbb R\to \mathbb R\) is a measurable function such that for almost all \(t\in T,\) \(j(t,\cdot)\) is locally Lipschitz. Applying the nonsmooth critical point theory, the authors obtain some results on the existence of a strictly positive and of multiple solutions.
generalized nonsmooth Palais-Smale condition
scientific article; zbMATH DE number 5144894
scientific article