Differential and Integral Equations

Existence of pseudo-symmetric solutions to a $p$-Laplacian four-point BVPs involving derivatives on time scales

Zhaosheng Feng and You-hui Su

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Abstract

We are concerned with a four-point boundary-value problem of the $p$-Laplacian dynamic equation on time scales where the nonlinear term contains the first-order derivatives of the dependent variable. By using Krasnosel'skii's fixed-point theorem, some new sufficient conditions are obtained for the existence of at least single or twin positive pseudo-symmetric solutions to this problem. We also establish the existence of at least triple or arbitrary odd positive pseudo-symmetric solutions to this problem by using the Avery-Peterson fixed-point theorem. As applications, two examples are given to illustrate and explain our main results.

Article information

Source
Differential Integral Equations, Volume 25, Number 5/6 (2012), 441-466.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012674

Mathematical Reviews number (MathSciNet)
MR2951736

Zentralblatt MATH identifier
1265.34340

Subjects
Primary: 34B15: Nonlinear boundary value problems 34L30: Nonlinear ordinary differential operators 35B09: Positive solutions 39A10: Difference equations, additive

Citation

Su, You-hui; Feng, Zhaosheng. Existence of pseudo-symmetric solutions to a $p$-Laplacian four-point BVPs involving derivatives on time scales. Differential Integral Equations 25 (2012), no. 5/6, 441--466. https://projecteuclid.org/euclid.die/1356012674


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