Nonnegativity of functionals corresponding to the second order half-linear differential equation

Robert Mařík

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 2, page 155-164
  • ISSN: 0044-8753

Abstract

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In this paper we study extremal properties of functional associated with the half–linear second order differential equation E p . Necessary and sufficient condition for nonnegativity of this functional is given in two special cases: the first case is when both points are regular and the second is the case, when one end point is singular. The obtained results extend the theory of quadratic functionals.

How to cite

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Mařík, Robert. "Nonnegativity of functionals corresponding to the second order half-linear differential equation." Archivum Mathematicum 035.2 (1999): 155-164. <http://eudml.org/doc/248354>.

@article{Mařík1999,
abstract = {In this paper we study extremal properties of functional associated with the half–linear second order differential equation E$_p$. Necessary and sufficient condition for nonnegativity of this functional is given in two special cases: the first case is when both points are regular and the second is the case, when one end point is singular. The obtained results extend the theory of quadratic functionals.},
author = {Mařík, Robert},
journal = {Archivum Mathematicum},
keywords = {half–linear differential equation; associated functional; Picone identity; conjugate points; half-linear differential equation; associated functional; Picone identity; conjugate points; extremal properties; regular functional; singular functional},
language = {eng},
number = {2},
pages = {155-164},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Nonnegativity of functionals corresponding to the second order half-linear differential equation},
url = {http://eudml.org/doc/248354},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Mařík, Robert
TI - Nonnegativity of functionals corresponding to the second order half-linear differential equation
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 2
SP - 155
EP - 164
AB - In this paper we study extremal properties of functional associated with the half–linear second order differential equation E$_p$. Necessary and sufficient condition for nonnegativity of this functional is given in two special cases: the first case is when both points are regular and the second is the case, when one end point is singular. The obtained results extend the theory of quadratic functionals.
LA - eng
KW - half–linear differential equation; associated functional; Picone identity; conjugate points; half-linear differential equation; associated functional; Picone identity; conjugate points; extremal properties; regular functional; singular functional
UR - http://eudml.org/doc/248354
ER -

References

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  1. On the second order half-linear differential equation, Studia Sci. Math. Hungar, 3 (1968), 411–437. (1968) Zbl0167.37403MR0267190
  2. On transformations of singular quadratic functionals corresponding to equation ( p y ' ) ' + q y = 0 , Arch. Math. (Brno) 24 (1988), 75–82. (1988) MR0983225
  3. Quadratic funtionals with general boundary conditions, Appl. Math. Opt. 36 (1997), 243–262. (1997) MR1457870
  4. A half-linear second order differential equation, Coll. Math. Soc. János Bolyai 30. Qual. theory of diff. eq. Szeged (Hungary) (1979), 153–179. (1979) 
  5. Theory of extremal problems, North-Holland Publ., 1979, pp. 122–124. (1979) MR0528295
  6. A Picone type identity for second order half-linear differential equations, (to appear). (to appear) MR1711081
  7. Global transformations of linear differential equations and quadratic functionals I,II, Arch. Math. 19 (1983), 161–171. (1983) MR0725199
  8. Singular quadratic functionals, Trans. Amer. Math. Soc. 40 (1936), 252–286. (1936) MR1501873
  9. Sturmian comparison theorem for half-linear second order diff. equations, Proc. Roy. Soc. of Edinburg 125 A (1995), 1193–1204. (1995) MR1362999
  10. Ordinary differential equations, John Wiley and Sons, New York, 1971. (1971) Zbl0212.10901MR0273082

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