V. Lakshmikantham's Differential and integral inequalities; Theory and PDF

By V. Lakshmikantham

ISBN-10: 0124110304

ISBN-13: 9780124110304

From the authors' preface: "This quantity constitutes the 1st a part of a monograph on concept and purposes of differential and indispensable inequalities. the most instruments for purposes are the Ljapunov services. the cloth of the current quantity is split into sections. the 1st part, which include 4 chapters, bargains with usual differential equations whereas the second one part is dedicated to Volterra critical equations.'' AMS evaluate via A. Halanay

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Soc. 4 (1897–1898), 295–313, 365–376. [18] , Le¸cons sur les m´ethodes de Sturm dans la th´ eorie des ´equations diff´ erentielles lin´eaires, et leurs d´eveloppements modernes, Gauthier-Villars, Paris, 1917. [19] O. Bolza, Lectures on the Calculus of Variations, Dover, New York, 1961. [20] M. Brown and M. Eastham, The Hurwitz theorem for Bessel functions and antibound states in spectral theory, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 459 (2003), 2431–2448. [21] R. Brown, S. Clark and D.

Math Soc. 42 (1974), 480–482. [71] A. Liapunov, Probl`eme G´en´eral de la Stabilit´e du Mouvement, (French translation of a Russian paper dated 1893), Ann. Fac. Sci. Univ. Toulouse 2 (1907), 27–247; reprinted as Ann. Math. Studies 17, Princeton, 1949. [72] H. Linden, Leighton’s bounds for Sturm-Liouville eigenvalues with eigenparameter in the boundary conditions, J. Math. Anal. Appl. 156 (1991), 444–456. [73] D. London, On the zeros of w (z) + p(z)w(z) = 0, Pacific J. Math. 12 (1962), 979–991. [74] J.

1) a over the class of admissible functions y defined as those sufficiently smooth y satisfying the endpoint conditions y(a) = A, y(b) = B. A necessary condition for an extremal is the vanishing of the first variation, dJ(y + η)/d =0 , for sufficiently smooth variations η satisfying η(a) = η(b) = 0. This leads to the Euler-Lagrange equation fy − d(fy )/dx = 0 for y. 2) a be positive for all nontrivial admissible η where p = fy y and q = fyy − d(fy y )/dx. 2) was related to the oscillation properties of −(py ) +qy = 0.

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Differential and integral inequalities; Theory and Applications Volume I: Ordinary differential equations by V. Lakshmikantham


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