- Understanding and applying the idea of the Dirichlet principle.
- Recognizing nonlinear differential equations in divergence form.
- Understanding the relationship between the Euler-Lagrange equation and variational problems.
- Understanding the relationship between Sobolev spaces and weak solutions of the Euler-Lagrange equation.
- Utilizing coercivity and convexity of the Lagrangian function to obtain the existence of weak solutions of the Euler-Lagrange equation.
- Using saddle point methods and Palais-Smale conditions to obtain the existence of weak solutions of the Euler-Lagrange equation.
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Dirichle principle, direct methods of the calculus of variations, critical point methods, Palais-Smale conditions. Existence theory for Euler-Lagrange equations.
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