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Article

Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems

School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
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Author to whom correspondence should be addressed.
Symmetry 2020, 12(12), 1989; https://doi.org/10.3390/sym12121989
Received: 14 November 2020 / Revised: 27 November 2020 / Accepted: 29 November 2020 / Published: 2 December 2020
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The main feature of obtained solutions (u(t),v(t)) is that the solution u(t) is positive, and the other solution v(t) may change sign. Finally, two examples with continuous function f1 being positive and f2 being semipositone are worked out to illustrate the main results. View Full-Text
Keywords: multiple solutions; fixed point theory; boundary value problems multiple solutions; fixed point theory; boundary value problems
MDPI and ACS Style

Lin, L.; Liu, Y.; Zhao, D. Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems. Symmetry 2020, 12, 1989. https://doi.org/10.3390/sym12121989

AMA Style

Lin L, Liu Y, Zhao D. Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems. Symmetry. 2020; 12(12):1989. https://doi.org/10.3390/sym12121989

Chicago/Turabian Style

Lin, Longfei, Yansheng Liu, and Daliang Zhao. 2020. "Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems" Symmetry 12, no. 12: 1989. https://doi.org/10.3390/sym12121989

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