Positive solutions for Sturm-Liouville eigenvalue problems
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Authors
Hua Su
- School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, 250014, Jinan, China.
Qiuju Tuo
- School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, 250014, Jinan, China.
Abstract
By means of the lower and upper solutions argument and fixed index theorem in the frame of the ODE technique, we consider the existence and nonexistence of multiple positive solutions for fourth-order eigenvalue
Sturm-Liouville boundary value problem. Our results significantly extend and improve many known results
including singular and nonsingular cases.
.
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ISRP Style
Hua Su, Qiuju Tuo, Positive solutions for Sturm-Liouville eigenvalue problems, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 1, 219--230
AMA Style
Su Hua, Tuo Qiuju, Positive solutions for Sturm-Liouville eigenvalue problems. J. Nonlinear Sci. Appl. (2016); 9(1):219--230
Chicago/Turabian Style
Su, Hua, Tuo, Qiuju. "Positive solutions for Sturm-Liouville eigenvalue problems." Journal of Nonlinear Sciences and Applications, 9, no. 1 (2016): 219--230
Keywords
- Fourth-order singular differential equation
- lower and upper solutions
- positive solutions
MSC
References
-
[1]
A. R. Aftabizadeh, Existence and uniqueness theorems for fourth order boundary value problem, J. Math. Anal. Appl., 116 (1986), 415-426.
-
[2]
R. P. Agarwal, M. Y. Chow, Iterative methods for a fourth order boundary value problem , J. Compu. Appl. Math., 10 (1984), 203-217.
-
[3]
G. Bonanno, B. Di Bella, A fourth-order boundary value problem for a Sturm-Liouville type equation, Appl. Math. Comput., 217 (2010), 3635-2940.
-
[4]
Y. Cui , J. X. Sun, Y. Zou, Global bifurcation and multiple results for Sturm-Liouville problems, J. Comput. Appl. Math., 235 (2011), 2185-2192.
-
[5]
D. J. Guo, V. Lakshmikantham , Nonlinear Problems in Abstract Cone, Academic Press Inc., New York (1988)
-
[6]
Y. S. Liu, Multiple positive solutions of nonlinear singular boundary value problem for fourth-order equations, Appl. Math. Lett., 17 (2004), 747-757.
-
[7]
R. Ma , Positive solutions of fourth-order two point boundary value problem, Ann. Differential Equation, 15 (1999), 305-313.
-
[8]
R. Ma, H. Wang , On the existence of positive solutions of fourth order ordinary differential equation, Appl. Anal., 59 (1995), 225-231.
-
[9]
Y. S. Yang, Fourth order two-point boundary value problem, Proc. Amer. Math. Soc., 104 (1988), 175-180.
-
[10]
J. Yang, Z. Wei, K. Liu , Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems , Appl. Math. Comput., 214 (2009), 424-432.
-
[11]
X. Zhang, Positive solutions for three-point semipositone boundary value problems with convex nonlinearity, J. Appl. Math. Comp., 30 (2009), 349-367.
-
[12]
Q. Zhang, F. Y. Li, X. Zhu, Multiple sign-changing solutions to the Sturm-Liouville boundary value problem with resonance, Appl. Math. Comput., 219 (2012), 1061-1072.
-
[13]
X. G. Zhang, L. Liu , Eigenvalues of fourth-order singular Sturm-Liouville boundary value problems, Nonlinear Anal., 68 (2008), 384-392.