01484nas a2200229 i 4500 acta88813 20251117160205.0 251117s2024 hu o 000 eng d 1417-3875 10.14232/ejqtde.2024.1.11 doi SZTE Egyetemi Kiadványok Repozitórium hun eng Quittner Pavol Necessary and sufficient conditions for one-dimensional variational problems with applications to elasticity [elektronikus dokumentum] / Quittner Pavol 2024 36 Electronic journal of qualitative theory of differential equations This paper deals with necessary and sufficient conditions for weak and strong minimizers of functionals Φ(u) = R b a f(x, u(x), u (x)) dx, where u ∈ C 1 ([a, b], RN). We first derive conditions which are simpler than the known ones, and then apply them to several particular problems, including stability problems in the elasticity theory. In particular, we solve some open problems in [A. Majumdar, A. Raisch, Stability of twisted rods, helices and buckling solutions in three dimensions, Nonlinearity 27(2014), 2841– 2867] by finding optimal conditions for the stability of a naturally straight Kirchhoff rod under various types of endpoint constraints. Természettudományok Matematika Differenciálegyenlet http://acta.bibl.u-szeged.hu/88813/1/ejqtde_2024_011.pdf Dokumentum-elérés