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Positive solution to a special singular second-order boundary value problem

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Qingliu YaoAuthors Info & Claims

Mathematical and Computer Modelling: An International Journal, Volume 47, Issue 11-12

Pages 1284 - 1291

https://doi.org/10.1016/j.mcm.2007.08.003

Published: 01 June 2008 Publication History

Abstract

Let @l be a nonnegative parameter. The existence of a positive solution is studied for a semipositone second-order boundary value problem u^''(t)=@lq(t)f(t,u(t),u^'(t)),@au(0)-@bu^'(0)=d,u(1)=0, where d>0,@a>=0,@b>=0,@a+@b>0, q(t)f(t,u,v)>=0 on a suitable subset of [0,1]x[0,+~)x(-~,+~) and f(t,u,v) is allowed to be singular at t=0,t=1 and u=0. The proofs are based on the Leray-Schauder fixed point theorem and the localization method.

References

[1]

Bobisud, L.E., O'Regan, D. and Royalty, W.D., Existence and nonexistence for a singular boundary value problem. Appl. Anal. v28. 245-256.

Crossref

Google Scholar

[2]

A note on existence of nonnegative solutions to singular semipositone problems. Nonlinear Anal. v36. 615-622.

Google Scholar

[3]

On the existence of nonnegative solutions of singular semipositone problems. Appl. Anal. v74. 351-362.

Google Scholar

[4]

Cheng, J., Positive solutions of singular semipositone problems. Acta Math. Sinica, Chinese Ser. v44. 673-678.

Google Scholar

[5]

Stane¿k, S., Positive solutions for a class of singular semipositone boundary value problems. Math. Comput. Model. v33. 353-361.

Digital Library

Google Scholar

[6]

Agarwal, R.P., On fourth order boundary value problems arising in beam analysis. Differential and Integral Equations. v2. 91-110.

Google Scholar

[7]

Yao, Q., Existence and multiplicity of positive radial solutions for a class of nonlinear elliptic equations in annular domains. Chinese Ann. Math., Chinese Ser. v22. 633-638.

Google Scholar

[8]

Yao, Q. and Feng, Y., The existence of solution for a third-order two-point boundary value problem. Appl. Math. Lett. v15. 227-232.

Crossref

Google Scholar

[9]

Yao, Q., Solution and positive solution to a class of semilinear third-order two-point boundary value problems. Appl. Math. Lett. v17. 1171-1175.

Crossref

Google Scholar

[10]

Yao, Q., Existence of n solutions and ¿ or positive solutions to a semipositone elastic beam equation. Nonlinear Anal. v66. 138-150.

Google Scholar

[11]

Yao, Q., Positive solutions of nonlinear second-order periodic boundary value problems. Appl. Math. Lett. v20. 583-590.

Crossref

Google Scholar

[12]

Spiegel, M.R., Theory and Problems of Real Variables. 1969. McGraw-Hill Book Company, New York, London, Toronto.

Google Scholar

Positive solution to a special singular second-order boundary value problem
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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cover image Mathematical and Computer Modelling: An International Journal

Mathematical and Computer Modelling: An International Journal Volume 47, Issue 11-12

June, 2008

335 pages

ISSN:0895-7177

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 June 2008

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