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Existence of Positive Solutions for Higher Order p-Laplacian Boundary Value Problems

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Abstract

In this paper, we consider a higher order p-Laplacian boundary value problem

$$\begin{aligned} (-1)^n[\phi _{p}(u^{(2n-2)}+k^2u^{(2n-4)})]''=f(t,u), ~~0\le t\le 1,\\ u^{(2i)}(0)=0=u^{(2i)}(1), ~~ 0\le i \le n-1, \end{aligned}$$

where \(n\ge 1\) and \(k\in (0, \frac{\pi }{2})\) is a constant. By applying fixed point index theory, we derive sufficient conditions for the existence of positive solutions to the boundary value problem.

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Acknowledgements

The authors thank the referees for their valuable comments.

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Authors and Affiliations

  1. Department of Applied Mathematics, Andhra University, Visakhapatnam, 530 003, India

    K. R. Prasad

  2. Department of Mathematics, GITAM (Deemed to be University), Visakhapatnam, 530 045, India

    N. Sreedhar

  3. Department of Mathematics, Jimma University, 378-Jimma, Oromia, Ethiopia

    L. T. Wesen

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  1. K. R. Prasad
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  2. N. Sreedhar
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  3. L. T. Wesen
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Correspondence to N. Sreedhar.

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Prasad, K.R., Sreedhar, N. & Wesen, L.T. Existence of Positive Solutions for Higher Order p-Laplacian Boundary Value Problems. Mediterr. J. Math. 15, 19 (2018). https://doi.org/10.1007/s00009-017-1064-x

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  • DOI: https://doi.org/10.1007/s00009-017-1064-x

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