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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On solvability of second-order Sturm-Liouville
boundary value problems at resonance


Author: Dong Yujun
Journal: Proc. Amer. Math. Soc. 126 (1998), 145-152
MSC (1991): Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-98-04212-9
MathSciNet review: 1443173
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Abstract: In this paper, based on of the concept $q_0\in H_0(p,(0,1),\alpha,\beta)$, which is a generalized form of the first resonant point $\pi^2$ to the Picard problem $x''+\lambda x=0$, $x(0)=x(1)=0$, we study the solvability of second-order Sturm-Liouville boundary value problems at resonance $(p(t)x')'+q_0(t)x+g(t,x)=h(t)$, $x(0){\cos \alpha}-p(0)x'(0)\sin \alpha=0$, $x(1)\cos \beta-p(1)x'(1)\sin \beta=0$, and improve the previous results about problems $x''+\pi^2x+g(t,x)=h(t),x(0)=x(1)=0$ derived by Chaitan P. Gupta, R.Iannacci and M. N. Nkashama, and Ma Ruyun, respectively.


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Additional Information

Dong Yujun
Affiliation: Institute of Mathematics, Jilin University, Changchun, Jilin, 130023, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-98-04212-9
Received by editor(s): May 9, 1996
Communicated by: Hal Smith
Article copyright: © Copyright 1998 American Mathematical Society