Leray-Schauder degree method in one-parameter functional boundary value problem

Svatoslav Staněk

Published: 1996-09-30

Vol. 10 (1996)

Leray-Schauder degree method in one-parameter functional boundary value problem

Svatoslav Staněk

Abstract

Sufficient conditions for the existence of solutions of one-parameter functional boundary value problems of the type
x" = f(t,x,x_t,x',x'_t,λ),
(x₀,x'₀) ∈ {(ϕ,χ+c); c∈R}, α(x|_J) = A, β(x(T)-x|_J) = B
are given. Here f: J×R×C_r×R×C_r×R→R is continuous, ϕ,χ∈C_r, α,β are continuous increasing functionals, A,B∈R and x|_J is the restriction of x to J=[0,T]. Results are proved by the Leray-Schauder degree method.

Keywords:

one-parameter boundary value problem , existence of solutions , Leray-Schauder degree , Borsuk theorem

Download files

PDF

Citation rules

Staněk, S. (1996). Leray-Schauder degree method in one-parameter functional boundary value problem. Annales Mathematicae Silesianae, 10, 111–125. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14198

Similar Articles

Zofia Muzyczka, On functional-differential equations with advancing argument , Annales Mathematicae Silesianae: Vol. 2 (1986)
Svatoslav Staněk, On the existence of two solutions of functional boundary value problems , Annales Mathematicae Silesianae: Vol. 14 (2000)
Milan Tvrdý, Linear boundary value problems for generalized differential equations , Annales Mathematicae Silesianae: Vol. 14 (2000)
Wojciech Surówka, A discrete form of Jordan curve theorem , Annales Mathematicae Silesianae: Vol. 7 (1993)
Tadeusz Dłotko, On periodic boundary value problem for a differential equation of n-th order , Annales Mathematicae Silesianae: Vol. 5 (1991)
Zdzisław Naniewicz, Magdalena Nockowska, On variational approach to economic equilibrium — type problem , Annales Mathematicae Silesianae: Vol. 20 (2006)
Zofia Muzyczka, On the existence of solutions of the differential equation with advanced argument , Annales Mathematicae Silesianae: Vol. 1 (1985)
Jan Ligęza, On a two point boundary value problem for linear differential equations of the fourth order in the colombeau algebra , Annales Mathematicae Silesianae: Vol. 15 (2001)
Maria Stolarczyk, On the existence of optimal control for general stochastic equations , Annales Mathematicae Silesianae: Vol. 3 (1990)
Binayak S. Choudhury, Nikhilesh Metiya, Sunirmal Kundu, Debashis Khatua, Existence, data dependence and stability of fixed points of multivalued maps in incomplete metric spaces , Annales Mathematicae Silesianae: Vol. 37 No. 1 (2023)

1 2 3 4 5 6 7 8 9 10 > >>

You may also start an advanced similarity search for this article.

References

1. F.M. Arscott, Two-parameter eigenvalue problems in differential equations, Proc. London Math. Soc. (3), 14, 1964, 459-470.
2. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin Heidelberg, 1985.
3. M. Greguš, F. Neuman, F.M. Arscott, Three-point boundary value problem in differential equations, J. London Math. Soc. (2), 3, 1971, 429-436.
4. P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.
5. A. Haščák, Disconjugacy and multipoint boundary value problems for linear differential equations with delay, Czech. Math. J., 39 (114), 1989, 70-77.
6. A. Haščák, Tests for disconjugacy and strict disconjugacy of linear differential equations with delays, Czech Math. J., 39 (114), 1989, 225-231.
7. A. Haščák, On the relationship between the initial and the multipoint boundary value problems for n-th order linear differential equations with delay, Archivum Math. (Brno), 26, 1990, 207-214.
8. S. Staněk, Three-point boundary value problem of retarded functional differential equation of the second order with parameter, Acta UP, Fac. rer. nat. 97, Math. XXIX, 1990, 107-121.
9. S. Staněk, Multi-point boundary value problems for a class of functional differential equations with parameter, Math. Slovaca, 42, No. 1, 1992, 85-96.
10. S. Staněk, Boundary value problems for one-parameter second-order differential equations, Ann. Math. Silesianae 7, Katowice 1993, 89-98.
11. S. Staněk, On a class of functional boundary value problems for second-order functional differential equations with parameter, Czech. Math. J. 43 (118), 1993, 339-348.
12. S. Staněk, Leray-Schauder degree method in functional boundary value problems depending on the parameter, Math. Nach. 164, 1993, 333-344.
13. S. Staněk, On certain three-point regular boundary value problems for nonlinear second-order differential equations depending on the parameter, Acta Univ. Palacki. Ołomuc., Fac. rer. mat., Math. 34, 1995, 155-166.
14. S. Staněk, On a class of functional boundary value problems for the equation x" = f(t,x,x',x",λ), Ann. Polon. Math. 59, 1994, 225-237. Google Scholar

Vol. 10 (1996)
Published: 1996-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit