Topological Methods in Nonlinear Analysis · 2000 · 15 citations · 5 references
Natural SciencesMathematicsDifferential EquationsBoundary ConditionsExistence TheoryPartial Differential EquationsVariational FormulationWeak FormulationDirichlet ProblemsDual Variational FormulationNonlinear Partial Differential EquationsNonlinear Variational FormulationNonlinear Variational ProblemsSecond-order Differential EquationsVariational Methods In Partial Differential EquationsVariational Problems
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.
5