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SOLVABILITY FOR SECOND-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS ON AN UNBOUNDED DOMAIN AT RESONANCE  

Yang, Ai-Jun (COLLEGE OF SCIENCE, ZHEJIANG UNIVERSITY OF TECHNOLOGY)
Wang, Lisheng (SCHOOL OF MATHEMATICS AND PHYSICS, JINGGANGSHAN UNIVERSITY)
Ge, Weigao (DEPARTMENT OF APPLIED MATHEMATICS, BEIJING INSTITUTE OF TECHNOLOGY)
Publication Information
The Pure and Applied Mathematics / v.17, no.1, 2010 , pp. 39-49 More about this Journal
Abstract
This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, $\infty$) with the boundary conditions $$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x where $g\;{\in}\;L^1[0,{\infty})$ with g(t) > 0 on [0, $\infty$) and ${\int}^{\infty}_0g(s)ds\;=\;1$, f is a g-Carath$\acute{e}$odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.
Keywords
integral boundary condition; unbounded domain; g-Carath$\acute{e}$odory function; resonance;
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1 W. Ge: Boundary value problems for ordinary nonlinear differential equations. Science Press, Beijing, 2007 (in Chinese).
2 R. P. Agarwal & D. O'Regan: Infinite interval problems for differential, diflerence and integral equations. Kluwer Academic, 2001.
3 A. Yang & W. Ge: Positive solutions of multi-point boundary value problems with multivalued operators at resonance. J. Appl. Math. Comput. On line: 10.1007/s12190-008-0217-2.
4 J.V. Baxley: Existence and uniqueness for nonlinear boundary value problems on infinite interval. J. Math. Anal. Appl. 147 (1990), 127-133.
5 A. Yang & W. Ge: Existence of symmetric solutions for a fourth-order multi-point boundary value problem with a p-Laplacian at resonance. J. Appl. Math. Comput. 29 (2009), no. 1, 301-309.   DOI
6 A. Yang, C. Miao & W. Ge: Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line. Elec. J. Qual. Theo. Diff. Equa. 15 (2009), 1-15.
7 H. Lian, H. Pang & W. Ge: Solvability for second-order three-point boundary value problems at resonance on a half-line. J. Math. Anal. Appl. 337 (2008), 1171-1181.   DOI   ScienceOn
8 N. Kosmatov: Multi-point boundary value problems on an unbounded domain at resonance. Nonlinear Anal. 68 (2008), 2158-2171.   DOI   ScienceOn
9 D. Jiang & R.P. Agarwal: A uniqueness and existence theorem for a singular thirdorder boundary value probIem on (0, $\infty$). Appl. Math. Lett. 15 (2002), 445-451.   DOI   ScienceOn
10 R. Ma: Existence of positive solution for second-order boundary value problems on infinite intervals. Appl. Math. Lett. 16 (2003), 33-39.   DOI   ScienceOn
11 S. Chen & Y. Zhang: Singular boundary value problems on a half-line. J. Math. Anal. Appl. 195 (1995), 449-468.   DOI   ScienceOn
12 B. Yan: Boundary value problems on the half-line with impulse and infinite delay. J. Math. Anal. Appl. 259 (2001), 94-114.   DOI   ScienceOn
13 J. Mawhin: Topological degree methods in nonlinear boundary value problems. in: NS-FCBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, 1979.