@article{article_1760600, title={Optimality Conditions for the Second-Order Semilinear Differential Inclusions of the Bolza Problem}, journal={Journal of Mathematical Sciences and Modelling}, volume={8}, pages={175–184}, year={2025}, DOI={10.33187/jmsm.1760600}, author={Çiçek, Gülseren and Bozcu Yüksek, Gülşah}, keywords={Boundary conditions, Discrete and differential inclusions, Euler-Lagrange inclusion, Locally adjoint mapping}, abstract={In this paper, optimality conditions for the Bolza problem with second-order semilinear differential inclusions (SDFIs) and initial conditions are derived. Despite its use in applications, there are few publications on this subject, and we hope to contribute to the literature. Locally adjoint mapping (LAM) is used to establish the adjoint discrete inclusion. Using the equivalence relations, necessary and sufficient conditions for the discrete approximation problem are formulated. By passing to the limit, sufficient optimality conditions are established for the optimal problem described by second-order SDFIs. Similar results for the non-convex problem are obtained by using the local tents. We provide an example of a semi-linear problem with initial conditions for which our results can be applied.}, number={4}, publisher={Mahmut AKYİĞİT}