Geodesic
NONTRIVIAL SOLUTIONS OF SINGULAR SECOND ORDER THERE-POINT BOUNDARY VALUE PROBLEM AT RESONANCEN  :
WU , XIAORONG 1   ; WANG, FENG 2
1 Department of Mathematics and Physics, Taizhou Teachers College, Taizhou, 225300, China.
2 School of Mathematics and Physics, Jiangsu Polytechnic University, Changzhou, 213164, China.
Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 1, p. 49-55 Cet article a éte moissonné depuis la source International Scientific Research Publications

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The singular second order three-point boundary value problem at resonance

$ \begin{cases} x''(t) = f(t, x(t)),\,\,\,\,\, 0 t 1,\\ x'(0) = 0, x(\eta) = x(1), \end{cases} $

are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where $\eta\in (0, 1)$ is a constant, $f$ is allowed to be singular at both $t = 0$ and $t = 1$. The existence results of nontrivial solutions are given by means of the topological degree theory.

DOI : 10.22436/jnsa.001.01.08
Classification : 34B15, 34B25
Keywords: Singular, Nontrivial solutions, Boundary value problem, Topology degree, Resonance.

WU , XIAORONG   1   ; WANG, FENG  2

1 Department of Mathematics and Physics, Taizhou Teachers College, Taizhou, 225300, China.
2 School of Mathematics and Physics, Jiangsu Polytechnic University, Changzhou, 213164, China. 
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WU , XIAORONG ; WANG, FENG. NONTRIVIAL SOLUTIONS OF SINGULAR SECOND ORDER THERE-POINT BOUNDARY VALUE PROBLEM AT RESONANCEN. Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 1, p. 49-55. doi: 10.22436/jnsa.001.01.08

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