Duality for multiobjective variational control and multiobjective fractional variational control problems with pseudoinvexity.

The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system $\{\begin{matrix} \ddot{u} (t) = \nabla F (t, u (t)), a.e. t \in [0, T], \\ u (0) - u (T) = \dot{u} (0) - \dot{u} (T) = 0 . \end{matrix}$ Some new existence theorems are obtained by the least action principle.

Existence of solutions for the Dirichlet problem with superlinear nonlinearities

Andrzej Nowakowski, Andrzej Rogowski (2003)

Czechoslovak Mathematical Journal

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In this paper we establish the existence of nontrivial solutions to $\frac{d}{d t} L_{x^{'}} (t, x^{'} (t)) + V_{x} (t, x (t)) = 0, x (0) = 0 = x (T),$ with $V_{x}$ superlinear in $x$ .

Solvability for a class of abstract two-point boundary value problems derived from optimal control.

Wang, Lianwen (2007)

Boundary Value Problems [electronic only]

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