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Existence of solutions for singular boundary problems for higher order differential equations

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Abstract

We offer sufficient conditions for the existence of solutions for the boundary value problem\(\begin{gathered} y(n) + f(t,y,y^1 ,...,y^{(n - 2)} = 0, 0< t< 1, n \geqslant 2 \\ y^{(i)} (0) = 0, 0 \leqslant i \leqslant n - 3 \\ y^{(n - 2)} (0) - \beta y^{(n - 1)} (0) = 0 \\ \gamma y^{(n - 2)} (1) + \delta y^{(n - 1)} (1) = 0 \\ \end{gathered} \) where α, β, γ and δ are constants satisfying αγ+αδ+βγ>0, β, δ≥0, β+α>0 and δ+γ>0.

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References

  1. Agarwal, R.P., Boundary Value Problems for Higher Order Differential Equations, World Scientific, Singapore, 1986.

    MATH  Google Scholar 

  2. Agarwal, R.P., Differential Equations and Inequalities, Marcel Dekker, New York, 1992.

    Google Scholar 

  3. Eloe, P.W. andHenderson, J.,Singular nonlinear boundary value problems for higher order ordinary differential equations, Nonlinear Analysis,17 (1991), 1–10.

    Article  MATH  MathSciNet  Google Scholar 

  4. Eloe, P.W. andHenderson, J.,Existence of solutions for some singular higher order boundary value problems, ZAMM,73 (1993), 315–323.

    Article  MATH  MathSciNet  Google Scholar 

  5. Gatica, J.A., Oliker, V. andWaltman, P.,Singular nonlinear boundary value problems for second-order ordinary differential equations, J. Diff. Eqs.,79 (1989), 62–78.

    Article  MATH  MathSciNet  Google Scholar 

  6. Henderson, J. andYin, K.C.,Singular boundary value problems, Bull. Inst. Math. Academia Sinica,19 (1991), 229–242.

    MATH  MathSciNet  Google Scholar 

  7. Henderson, J.,Singular boundary value problems for difference equations, Dynamic Systems and Applications,1 (1992), 271–282.

    MATH  MathSciNet  Google Scholar 

  8. Henderson, J.,Singular boundary value problems for higher order difference equations, in Proceedings of the First World Congress of Nonlinear Analysis, ed V. Lakshmikantham, Walter de Gruyter and Co., in press.

  9. Henderson, J. andYin, K.C.,Focal boundary value problems for singular ordinary differential equations, Advances in Nonlinear Dynamics, in press.

  10. Kong L.B. andWang, J.Y.,A remark on some singular nonlinear higher order boundary value problems, ZAMM, in press.

  11. Wang, J.,A singular nonlinear boundary value problem for a higher order ordinary differential equation, Nonlinear Analysis,22 (1994), 1051–1056.

    Article  MATH  MathSciNet  Google Scholar 

  12. Wong, P.J.Y. andAgarwal, R.P.,On the existence of solutions of singular value problems for higher order difference equations, Nonlinear Analysis, to appear.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Singapore

    Ravi P. Agarwal

  2. Division of Mathematics, Nanyang Technological University, Singapore

    Patricia J. Y. Wong

Authors
  1. Ravi P. Agarwal
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  2. Patricia J. Y. Wong
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Conferenza tenuta da R.P. Agarwal il 19 giugno 1995

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Agarwal, R.P., Wong, P.J.Y. Existence of solutions for singular boundary problems for higher order differential equations. Seminario Mat. e. Fis. di Milano 65, 249–264 (1995). https://doi.org/10.1007/BF02925259

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