Geodesic
A degree theory for Lagrangian boundary value problems
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 1, pp. 5-25

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We study those nonlinear partial differential equations which appear as Euler–Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems.
Keywords: nonlinear equations, Lagrangian system, weak boundary values, quasilinear Fredholm operators, mapping degree. 
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     title = {A degree theory for {Lagrangian} boundary value problems},
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Ammar Alsaedy; Nikolai Tarkhanov. A degree theory for Lagrangian boundary value problems. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 1, pp. 5-25. http://geodesic.mathdoc.fr/item/JSFU_2020_13_1_a0/