An application of Schauder's fixed point theorem with respect to higher order BVPs
Author:
FuHsiang Wong
Journal:
Proc. Amer. Math. Soc. 126 (1998), 23892397
MSC (1991):
Primary 34B15
MathSciNet review:
1476399
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: We shall provide conditions on the function . The higher order boundary value problem has at least one solution.
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 R. P. Agarwal and F. H. Wong, Existence of positive solutions for higher order boundary value problems, Nonlinear Studies, to appear.
 [2]
 R. P. Agarwal and F. H. Wong, Existence of positive solutions for nonpositive higher order BVP's, to appear in Computational and Applied Mathematics.
 [3]
 R. P. Agarwal and F. H. Wong, An application of topological transervality with respect to nonpositive higher order BVP's, to appear.
 [4]
 V. Anuradha, D. D. Hai and R. Shivaji, Existence results for superlinear semipositive BVP's, Proc. Amer. math. Soc 124 (1996), 757763. MR 96f:34030
 [5]
 P. B. Bailey, L. F. Shampine and P. E. Waltman, Nonlinear Twopoint Boundary Value Problems, Academic Press, New York, 1968. MR 37:6524
 [6]
 C. Bandle and M.K. Kwong, Semilinear elliptic problems in annular domains, Z. Angew. Math. Phys. 40 (1989), 245257. MR 90m:35062
 [7]
 Y. S. Choi and G. S. Ludford, An unexpected stability result of the nearextinction diffusion flame for nonunity Lewis numbers, Q. J. Mech. Appl. Math 42 part 1 (1989), 143158. MR 91b:80022
 [8]
 C. J. Chyan and J. Henderson, Positive solutions for singular higher order nonlinear equations, Diff. Eqns. Dyn. Sys 2 (1994), 153160. MR 97b:34017
 [9]
 E. N. Dancer, On the structure of solutions of an equation in catalysis theory when a parameter is large, J. Diff. Eqns 37 (1980), 404437. MR 82b:35018
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 H. Dang and K. Schmitt, Existence of positive solutions for semiliear elliptic equations in annular domain, Diff. and Integ. Equs. 7 (1994), 747758. MR 94m:35020
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 K. Deimling, Nonlinear functional analysis, Springer, New York, 1985. MR 86j:47001
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 L. H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994), 743748. MR 94e:34025
 [14]
 X. Garaizar, Existence of positive radial solutions for semiliear elliptic equations in the annulus, J. Differential Equations 70 (1987), 6972. MR 89f:35019
 [15]
 A. Granas, R. B. Guenther and J. W. Lee, On a theorem of S. Bernstein, Pac. Jour. Math. 73 (1977), 116. MR 57:10068
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 A. Granas, R. B. Guenther and J. W. Lee, Nonlinear boundary value problems for some classes of ordinary differential equations, Rocky Mount. J. Math. 10 (1980), 3558. MR 81h:34017
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 J. Henderson, Singular boundary value problems for difference equations, Dynamic Systems and Applications 1 (1992), 271282. MR 94a:39004
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 P. Kelevedjiev, Existence of solutions for twopoint boundary value problems, Nonlinear Analysis T. M. & A. 22 (1994), 217224. MR 95a:34029
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 P. Kelevedjiev, Nonexistence of solutions for twopoint boundary value problems, Nonlinear Analysis T. M. & A. 22 (1994), 225228. MR 95a:34030
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 M. A. Krasnoselskii, Positive solutions of operator equations, Noordhoff, Groningen, 1964. MR 31:6107
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 J. W. Lee and D. O'Regan, Nonlinear boundary value problems in Hilbert spaces, Jour. Math. Anal. Appl. 137 (1989), 5969. MR 90a:34048
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 J. Mawhin, Topological degree and boundary value problems for nonlinear differential equations, NSFCB Regional Conference Series in Math., vol. No. 40, Amer. Math. Soc., Providence. R. I., 1979.
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 N. Vasilev and I. Klokov, Bases of the theory of boundary value problems for ordinary differential equations, Izdat ``Zinatne.'' Riga, 1978.
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 H. Wang, On the existence of positive solutions for semilinear elliptic equations in the annulus, J. Differential Equations 109 (1994), 17. MR 95c:35093
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 F. H. Wong, Existence of positive solutions of singular boundary value problems, Nonlinear Analysis T.M.& A. 21 (1993), 397406. MR 94i:34056
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Additional Information
FuHsiang Wong
Affiliation:
Department of Mathematics and Science, National Taipei Teacher’s College, 134, HoPing E. Rd. Sec. 2, Taipei 10659, Taiwan, Republic of China
Email:
wong@tea.ntptc.edu.tw
DOI:
http://dx.doi.org/10.1090/S0002993998047091
PII:
S 00029939(98)047091
Keywords:
Higher order boundary value problems,
solution,
operator equation,
Green's function,
Schauder's fixed point theorem,
upperlowersolutions
Received by editor(s):
January 22, 1997
Communicated by:
Hal L. Smith
Article copyright:
© Copyright 1998
American Mathematical Society
