Positive solutions for a fourth-order p-Laplacian boundary value problem

Author:

Graef John R.1ORCID,Yang Bo2

Affiliation:

1. Department of Mathematics , University of Tennessee at Chattanooga , Chattanooga , TN 37403 , USA

2. Department of Mathematics , Kennesaw State University , Kennesaw , GA 30144 , USA

Abstract

Abstract The authors consider a fourth-order boundary value problem with a p-Laplacian appearing in both the equation and the boundary conditions. Upper and lower estimates for positive solutions to the problem are proved. Sufficient conditions for the existence and nonexistence of positive solutions to the problem are obtained and illustrated with an example.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference23 articles.

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2. J. Benedikt, P. Girg, L. Kotrla and P. Takáč, Origin of the p-Laplacian and A. Missbach, Electron. J. Differential Equations 2018 (2018), Paper No. 16.

3. N. Benkaci-Ali and A. Benmezai, Positive solution for fourth order four-point BVPs involving weighted p ⁢ ( t ) p(t) -Laplacian like operator, J. Adv. Res. Dyn. Control Syst. 6 (2014), no. 2, 64–76.

4. Y. P. Chen and B. X. Jin, Positive solutions of singular fourth-order four-point boundary value problems with p-Laplacian operator, Acta Anal. Funct. Appl. 14 (2012), no. 2, 147–156.

5. F. T. Fen and I. Y. Karaca, Positive solutions for a fourth-order multipoint impulsive BVP with p-Laplacian on time scales, Dynamic Systems and Applications. Vol. 7, Dynamic, Atlanta (2016), 83–89.

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