Nonlinear boundary value problems of the calculus of variations

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2003, 2003(Special): 760-770. doi: 10.3934/proc.2003.2003.760

Nonlinear boundary value problems of the calculus of variations

1.	Institute of Mathematics and Computer Science, University of Latvia, Rainis boul. 29, LV-1459 Riga, Lativa, United States

Received September 2002 Revised May 2003 Published April 2003

Abstract
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We consider nonlinear boundary value problems arising in the classical one-dimensional calculus of variations for scalar-valued unknown functions. Conditions for the existence of extremals (solutions of the Euler equation subject to related boundary conditions) are obtained and properties of extremals are discussed. The method of upper and lower solutions (functions) is our main tool. Several Bernstein - Nagumo type conditions are derived directly in terms of the Lagrangian. Both coercive and non-coercive (slow-growth) variational problems are considered.

Keywords: extremals, regularity of solutions., basic problem of the calculus of variations, Nonlinear boundary value problems, free end point problem.

Mathematics Subject Classification: Primary: 34B15, 49N60; Secondary: 49K0.

Citation: Felix Sadyrbaev. Nonlinear boundary value problems of the calculus of variations. Conference Publications, 2003, 2003 (Special) : 760-770. doi: 10.3934/proc.2003.2003.760

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