## Theses on the calculus of variations submitted to the faculty of the Division of the physical sciences in candidacy for the degree of doctor of philosophy, Department of mathematics |

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### Contents

ABALOQUB 07 THB 1S0B C0HDITI0H8 FOB THE 180 | 29 |

Y COHDITIOHS ON THB M2BXBXZXBQ F0HCTI0B3 ALOHO | 36 |

HA30N FUNDAMENTAL LEMMA | 45 |

8 other sections not shown

### Common terms and phrases

admissible arc admissible variations analogue arguments boundary value problem calculus of variations characteristic numbers coefficients conjugate points constants continuous corner corollary corresponding curve deduced defined definition determinant different from zero differential equations discontinuous double integral exists expression extremal extremaloid finite number focal point follows func functions of lines funotions funotlons fy.y given Hence Henoe hypotheses identically zero inequality integrand interval Lagrange problem lemma linear linearly independent Linoei manifold matrix maxima and minima maximizing arc minimizing arc minimizing surface minimum monopoly problem multiplier rule necessary condition neighborhood normal oaloulus olass one-parameter family ourve parameter partial derivatives problem of Lagrange problem of Mayer problem of minimizing proof properties quadratic form respect Riesz theorem satisfy the equations satisfying the conditions semi-extremal Sinoe Stieltjes integrals Stourgeon sufficient conditions suoh theorem theory tions vanish variables Volterra derivative whioh whloh x^Xg