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Positive solutions to semi-positone fourth-order \(\phi \)-Laplacian BVPs

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Abstract

This work is devoted to proving existence of positive solutions to a fourth-order semipositone \(\phi \)-Laplacian boundary problem. The nonlinearity may have time-singularity and change sign. Existence results are proved using the Krasnosel’skii and the Leggett-Williams fixed point theorems and examples of applications are provided.

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References

  1. Agarwal, R.P.: On fourth order boundary value problems arising in beam analysis. Differ. Integral Equ. 2(1), 91–110 (1989)

    MathSciNet  MATH  Google Scholar 

  2. Bai, Z., Wang, H.: On positive solutions of some nonlinear fourth-order beam equations. J. Math. Anal. Appl. 270(2), 357–368 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Benmezai, A., Djebali, S., Moussaoui, T.: Multiple positive solutions for \(\phi \)-Laplacian BVPs. Panam. Math. J. 17(3), 53–73 (2007)

    MathSciNet  MATH  Google Scholar 

  4. Djebali, S., Moussaoui, T., Precup, R.: Fourth order \(p\)-laplacian nonlinear systems via the vector version of the Krasnosel’skiĭ’s fixed point theorem. Mediterr. J. Math. 6(4), 447–460 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering, 5. Academic Press Inc, Boston (1988)

    Google Scholar 

  6. Gupta, C.P.: Existence and uniqueness theorems for the bending of an elastic beam equation. Appl. Anal. 26(4), 289–304 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  7. Krasnosel’skii, M.A.: Positive Solutions of Operator Equations, Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron P. Noordhoff Ltd. Groningen (1964)

  8. Leggett, R.W., Williams, L.R.: Multiple positive fixed points of nonlinear operators on ordred Banach spaces. Indiana Univ. Math. J. 28(4), 673–688 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu, B.: Positive solutions of fourth-order two point boundary value problems. Appl. Math. Comput. 148(2), 407–420 (2004)

    MathSciNet  MATH  Google Scholar 

  10. Ma, R., Wang, H.: On the existence of positive solutions of fourth-order ordinary differential equations. Anal. Appl. 59(1–4), 225–231 (1995)

    MathSciNet  MATH  Google Scholar 

  11. Song, R., Lü, H.: Positive solutions for singular nonlinear beam equation. Electron. J. Differ. Equ. 3, 9 (2007). (electronic)

    MathSciNet  MATH  Google Scholar 

  12. Yang, Y.: Fourth-order two-point boundary value problem. Proc. Am. Math. Soc. 104(1), 175–180 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhu, Y., Weng, P.: Multiple positive solutions for a fourth-order boundary value problem. Bol. Soc. Parana. Mat. 21(1–2), 9–19 (2003)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departement of Mathematics and Informatics, Faculty of Sciences, University Alger 1, Algiers, Algeria

    Kamel Bachouche

  2. Laboratory of Fixed Point Theory and Applications, École Normale Supérieure, Kouba, BP 92, 16006, Algiers, Algeria

    Kamel Bachouche, Abdelhamid Benmezai & S. Djebali

  3. Faculty of Mathematics, USTHB, El Alia, BP 32, 16111, Algiers, Algeria

    Abdelhamid Benmezai

  4. Department of Mathematics, Faculty of Sciences, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh, 11623, Saudi Arabia

    S. Djebali

Authors
  1. Kamel Bachouche
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  2. Abdelhamid Benmezai
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  3. S. Djebali
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Correspondence to S. Djebali.

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Bachouche, K., Benmezai, A. & Djebali, S. Positive solutions to semi-positone fourth-order \(\phi \)-Laplacian BVPs. Positivity 21, 193–212 (2017). https://doi.org/10.1007/s11117-016-0415-3

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  • DOI: https://doi.org/10.1007/s11117-016-0415-3

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