The reduction of certain boundary value problems to variational problems by means of transversality conditions

1970 ◽  
Vol 15 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Hanno Rund
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Variational Problems ◽  
Transversality Conditions

scholarly journals A Degree Theory for Lagrangian Boundary Value Problems

2020 ◽  
pp. 5-25
Author(s):  
Ammar Alsaedy ◽  
Nikolai Tarkhanov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlinear Partial Differential Equations ◽  
Degree Theory ◽  
Variational Problems ◽  
Boundary Values ◽  
Lagrange Equations ◽  
Lagrangian Boundary

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

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