Dependence on parameters for the Dirichlet problem with superlinear nonlinearities

Abstract

The nonlinear second order differential equation $$ \frac{d}{dt} h(t,x'(t))+g(t,x(t))=0, \quad t\in[0,T] \text{ a.e. } \quad x'(0)=x'(T)=0 $$ with superlinear function $g$ is investigated. Based on dual variational method the existence of solution is proved. Dependence on parameters and approximation method are also presented.