On solvability of nonlinear boundary value problems for the equation with one-sided growth restrictions on
Archivum Mathematicum (2002)
- Volume: 038, Issue: 2, page 129-148
- ISSN: 0044-8753
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topStaněk, Svatoslav. "On solvability of nonlinear boundary value problems for the equation $(x^{\prime }+g(t,x,x^{\prime }))^{\prime }=f(t,x,x^{\prime })$ with one-sided growth restrictions on $f$." Archivum Mathematicum 038.2 (2002): 129-148. <http://eudml.org/doc/248953>.
@article{Staněk2002,
abstract = {We consider boundary value problems for second order differential equations of the form $(x^\{\prime \}+g(t,x,x^\{\prime \}))^\{\prime \}=f(t,x,x^\{\prime \})$ with the boundary conditions $r(x(0),x^\{\prime \}(0),x(T)) + \varphi (x)=0$, $w(x(0),x(T),x^\{\prime \}(T))+ \psi (x)=0$, where $g,r,w$ are continuous functions, $f$ satisfies the local Carathéodory conditions and $\varphi , \psi $ are continuous and nondecreasing functionals. Existence results are proved by the method of lower and upper functions and applying the degree theory for $\alpha $-condensing operators.},
author = {Staněk, Svatoslav},
journal = {Archivum Mathematicum},
keywords = {nonlinear boundary value problem; existence; lower and upper functions; $\alpha $-condensing operator; Borsuk antipodal theorem; Leray-Schauder degree; homotopy; nonlinear boundary value problem; existence; lower and upper functions; -condensing operator; Borsuk antipodal theorem; Leray-Schauder degree; homotopy},
language = {eng},
number = {2},
pages = {129-148},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On solvability of nonlinear boundary value problems for the equation $(x^\{\prime \}+g(t,x,x^\{\prime \}))^\{\prime \}=f(t,x,x^\{\prime \})$ with one-sided growth restrictions on $f$},
url = {http://eudml.org/doc/248953},
volume = {038},
year = {2002},
}
TY - JOUR
AU - Staněk, Svatoslav
TI - On solvability of nonlinear boundary value problems for the equation $(x^{\prime }+g(t,x,x^{\prime }))^{\prime }=f(t,x,x^{\prime })$ with one-sided growth restrictions on $f$
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 2
SP - 129
EP - 148
AB - We consider boundary value problems for second order differential equations of the form $(x^{\prime }+g(t,x,x^{\prime }))^{\prime }=f(t,x,x^{\prime })$ with the boundary conditions $r(x(0),x^{\prime }(0),x(T)) + \varphi (x)=0$, $w(x(0),x(T),x^{\prime }(T))+ \psi (x)=0$, where $g,r,w$ are continuous functions, $f$ satisfies the local Carathéodory conditions and $\varphi , \psi $ are continuous and nondecreasing functionals. Existence results are proved by the method of lower and upper functions and applying the degree theory for $\alpha $-condensing operators.
LA - eng
KW - nonlinear boundary value problem; existence; lower and upper functions; $\alpha $-condensing operator; Borsuk antipodal theorem; Leray-Schauder degree; homotopy; nonlinear boundary value problem; existence; lower and upper functions; -condensing operator; Borsuk antipodal theorem; Leray-Schauder degree; homotopy
UR - http://eudml.org/doc/248953
ER -
References
top- Cabada A., Pouso R. L., Existence results for the problem with nonlinear boundary conditions, Nonlinear Anal. 35 (1999), 221–231. (1999) MR1643240
- Deimling K., Nonlinear Functional Analysis, Springer-Verlag, Berlin Heidelberg, 1985. (1985) Zbl0559.47040MR0787404
- Kiguradze I. T., Boundary Value Problems for Systems of Ordinary Differential Equations, In “Current Problems in Mathematics: Newest Results", Vol. 30, 3–103, Moscow 1987 (in Russian); English transl.: J. Soviet Math. 43 (1988), 2340–2417. (1987) Zbl0782.34025MR0925829
- Kiguradze I. T., Lezhava N. R., Some nonlinear two-point boundary value problems, Differentsial’nyie Uravneniya 10 (1974), 2147–2161 (in Russian); English transl.: Differ. Equations 10 (1974), 1660–1671. (1974) MR0364733
- Kiguradze I. T., Lezhava N. R., On a nonlinear boundary value problem, Funct. theor. Methods in Differ. Equat., Pitman Publ. London 1976, 259–276. (1976) Zbl0346.34008MR0499409
- Staněk S., Two-point functional boundary value problems without growth restrictions, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 37 (1998), 123–142. (1998) Zbl0963.34061MR1690481
- Thompson H. B., Second order ordinary differential equations with fully nonlinear two point boundary conditions, Pacific. J. Math. 172 (1996), 255–277. (1996) Zbl0862.34015MR1379297
- Thompson H. B., Second order ordinary differential equations with fully nonlinear two point boundary conditions II, Pacific. J. Math. 172 (1996), 279–297. (1996) Zbl0862.34015MR1379297
- Wang M. X., Cabada A., Nieto J. J., Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions, Ann. Polon. Math. 58 (1993), 221–235. (1993) Zbl0789.34027MR1244394
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