On positive solutions for a nonlinear boundary value problem with impulse

Huseyin Bereketoglu; Aydin Huseynov

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 1, page 247-265
  • ISSN: 0011-4642

Abstract

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In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.

How to cite

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Bereketoglu, Huseyin, and Huseynov, Aydin. "On positive solutions for a nonlinear boundary value problem with impulse." Czechoslovak Mathematical Journal 56.1 (2006): 247-265. <http://eudml.org/doc/31026>.

@article{Bereketoglu2006,
abstract = {In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.},
author = {Bereketoglu, Huseyin, Huseynov, Aydin},
journal = {Czechoslovak Mathematical Journal},
keywords = {impulse conditions; Green’s function; completely continuous operator; fixed point theorem in cones; impulse conditions; Green's function; completely continuous operator; fixed point theorem in cones},
language = {eng},
number = {1},
pages = {247-265},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On positive solutions for a nonlinear boundary value problem with impulse},
url = {http://eudml.org/doc/31026},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Bereketoglu, Huseyin
AU - Huseynov, Aydin
TI - On positive solutions for a nonlinear boundary value problem with impulse
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 1
SP - 247
EP - 265
AB - In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.
LA - eng
KW - impulse conditions; Green’s function; completely continuous operator; fixed point theorem in cones; impulse conditions; Green's function; completely continuous operator; fixed point theorem in cones
UR - http://eudml.org/doc/31026
ER -

References

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  1. 10.1016/S0377-0427(00)00438-6, J. Comput. Appl. Math. 132 (2001), 341–356. (2001) MR1840633DOI10.1016/S0377-0427(00)00438-6
  2. Impulsive Differential Equations: Asymtotic Properties of the Solutions, World Scientific, Singapore, 1995. (1995) MR1331144
  3. Positive solutions of boundary value problems for ordinary differential equations with impulse, Dynam. Contin. Discrete Impuls. Systems 4 (1998), 285–294. (1998) MR1621834
  4. Positive solutions and conjugate points for a boundary value problem with impulse, Dynam. Systems Appl. 7 (1998), 441–449. (1998) MR1664566
  5. 10.1006/jmaa.1994.1227, J. Math. Anal. Appl. 184 (1994), 640–648. (1994) MR1281534DOI10.1006/jmaa.1994.1227
  6. 10.1090/S0002-9939-1994-1204373-9, Proc. Amer. Math. Soc. 120 (1994), 743–748. (1994) MR1204373DOI10.1090/S0002-9939-1994-1204373-9
  7. Nonlinear Problems in Abstract Cones, Academic Press, San Diego, 1998. (1998) MR0959889
  8. Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964. (1964) MR0181881
  9. Lineare Differential Operatoren, Akademie-Verlag, Berlin, 1967. (1967) 
  10. Impulsive Differential Equations, World Scientific, Singapore, 1995. (1995) MR1355787
  11. Differential and Integral Equations: Boundary Value Problems and Adjoint, Academia and Reidel, Praha and Dordrecht, 1979. (1979) MR0542283
  12. Generalized Ordinary Differential Equations, World Scientific, Singapore, 1992. (1992) Zbl0781.34003MR1200241
  13. Differential and integral equations in the space of regulated functions, Memoirs on Differential Equations and Mathematical Physics 25 (2002), 1–104. (2002) MR1903190
  14. Linear distributional differential equations of the second order, Math. Bohem. 119 (1994), 415–436. (1994) MR1316594

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