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Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations


Authors: John R. Graef, Chuanxi Qian and Bo Yang
Journal: Proc. Amer. Math. Soc. 131 (2003), 577-585
MSC (2000): Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-02-06579-6
Published electronically: June 18, 2002
MathSciNet review: 1933349
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the authors consider the boundary value problem

\begin{displaymath}({E}) \ \qquad\qquad\quad x^{(2m)}(t)+(-1)^{m+1} f(x(t))=0, \quad 0<t<1, \qquad\qquad\quad\, \ \ \end{displaymath}


\begin{displaymath}({B}) \qquad\qquad \ x^{(2i)}(0)=x^{(2i)}(1)=0, \quad i=0,1,2,\cdots,m-1, \ \qquad\qquad \ \ \end{displaymath}

and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)-(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373-2379) are discussed.


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Additional Information

John R. Graef
Affiliation: Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee 37403
Email: john-graef@utc.edu

Chuanxi Qian
Affiliation: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
Email: qian@math.msstate.edu

Bo Yang
Affiliation: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
Email: by2@ra.msstate.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06579-6
Keywords: Boundary value problems, existence of positive solutions, higher order equations, multiple solutions, nonlinear equations
Received by editor(s): April 16, 2001
Received by editor(s) in revised form: October 2, 2001
Published electronically: June 18, 2002
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society

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