共振情形下四阶p-Laplace方程四点边值问题

Abstract

Abstract:

This paper deals with the fourth order boundary value problem with p-Laplace at resonance
(φ_'p(u′′(t)))′′ = f(t, u(t), u′(t), u′′(t)), 0 < t < 1,
u(0) = 0, u(1) = au(ξ), u′′(0) = 0, u′′(1) = bu′′(η),
where 0 < ξ，η < 1; a, b > 0 such that a ξ = 1 and b^p⁻¹η ≤ 1. The existence of solutions is obtained by means of Mawhin’s continuation theorem.

Key words: Fourth order boundary value problem, p-Laplace equation, Resonance, Theory of coincidence degree

CLC Number:

34B15

Cite this article

JIN Shan, LU Shi-Ping. Existence of Solutions for Fourth Order Boundary Value Problem with p-Laplace at Resonance[J].Acta mathematica scientia,Series A, 2011, 31(3): 829-836.

share this article

0
/ / Recommend

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://121.43.60.238/sxwlxbA/EN/

http://121.43.60.238/sxwlxbA/EN/Y2011/V31/I3/829

Trendmd

References

[1] Bernis F. Compactness of the support in convex and non-convex fourth order elasticity problems. Nonlinear
Anal, 1982, 6: 1221–1243

[2] Agarwal P R, L¨u H S, O’Regan D. Positive solutions for the boundary value problem (|u′′|p−2u′′)′′ −q(t)f(u(t)) = 0. Mem Differential Equations Math Phys, 2003, 28: 33–44

[3] Jiang D Q, Liu H Z, Xu X J. Nonresonant singular fourth-order boundary value problems. Appl Math Lett, 2005, 18: 69–75

[4] Bai Z B. Existence and multiplicity of positive solutions for a fourth-order p-Laplace equations. Appl Math Mech, 2001, 22: 1476–1480

[5] Jin Shan, Zhang Zhirong, Lu Shiping. Existence of soluation for a fourth order p-Laplace equation boundary
value problem. Journal of Jinlin University (science edition) (in Chinese), 2008, 46(2): 214–218

[6] Bai Z B, Ge W G. The iterative solutions for some fourth-order p-Laplace equation boundary value problems. Appl Math Lett, 2006, 19: 8–14

[7] Guo Y, Ge W G. Positive solutions for three-point boundary value problems with dependence on the first order derivative. J Math Anal Appl, 2004, 290: 291–301

[8] Gaines R E, Mawhin J L. Coincidence Degree and Nonlinear Differential Equations. Berlin: Springer, 1977

Related Articles 12

[1]	Ouyang Cheng, Mo Jiaqi. Study of Nonlinear Duffing Disturbed Oscillator for Resonance Mechanism [J]. Acta mathematica scientia,Series A, 2018, 38(1): 190-196.
[2]	Ling Zhengqiu, Wang Zejia. Blow-Up Questions of Solutions to a Class of p-Laplace Equation with Dissipative Gradient Term [J]. Acta mathematica scientia,Series A, 2016, 36(5): 958-964.
[3]	Liang Yunyun, Zhu Zeqi, Zhao Min, Zhao Caidi. Finite Fractal Dimension of Kernel Sections for Long-Wave-Short-Wave Resonance Equations on Infinite Lattices [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1146-1157.
[4]	Deng Yihua, Luo Liping, Zhou Lijun. Existence of A Ground State Solution for A Class of Superlinear p-Laplace Equations with Negative Potential Functions [J]. Acta mathematica scientia,Series A, 2015, 35(3): 578-586.
[5]	HU Lei, ZHANG Shu-Qin, SHI Ai-Ling. Existence of \|Solutions for Two-point Boundary Value Problem of a Coupled Fractional Differential Equations at Resonance [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1313-1326.
[6]	SONG Ming-Liang. Resonance Theorems for Families of Pointwise Semi-bounded and Non-unbounded Linear Operators on F* Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1071-1082.
[7]	ZENG Xiao-Yu, WAN Jun-Xia. The Existence of \|Solution for p-Laplace Equation Involving Resonant Term [J]. Acta mathematica scientia,Series A, 2014, 34(2): 227-233.
[8]	PEI Rui-Chang. Nontrivial Solutions for p-Laplacian Dirichlet Problem [J]. Acta mathematica scientia,Series A, 2013, 33(1): 165-173.
[9]	WANG Feng, SUN Jing-Xian, CUI Yu-Jun. Positive Solutions of a Class of Operator Equations Lx=Nx [J]. Acta mathematica scientia,Series A, 2010, 30(1): 278-288.
[10]	LI Yong-Xiang, YANG He. Two-Parameter Nonresonance Condition Described by Ellipse for Fourth-order Boundary Value Problems [J]. Acta mathematica scientia,Series A, 2010, 30(1): 239-244.
[11]	Liu Xiangqing; Huang Yisheng. A Class of Quasilinear Elliptic Equations with Weights [J]. Acta mathematica scientia,Series A, 2007, 27(2): 277-287.
[12]	LI Yong-Xiang. Existence and Method of Lower and Upper Solutions for Fourth Order Nonlinear Boundary Value Problems [J]. Acta mathematica scientia,Series A, 2003, 23(2): 245-252.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	Wei Xuemei, Cui Shangbin. Existence and Uniqueness of Global Solutions of a Free Boundary Problem Modeling Tumor Growth[J]. Acta mathematica scientia,Series A, 2006, 26(1): 1 -008 .
[2]	Deng Guantie. Factorization of Analytic Function of Order Less Than[J]. Acta mathematica scientia,Series A, 2007, 27(1): 1 -006 .
[3]	Yao Qingliu. Multiple Positive Solutions to a Singular Beam Equation Fixed at Both Ends[J]. Acta mathematica scientia,Series A, 2008, 28(4): 768 -778 .
[4]	Jiang Jiao; Xu Jianhua; Han Maoan. Periodic Solutions of Neutral Integro-Differential Equations with Infinite Delay[J]. Acta mathematica scientia,Series A, 2008, 28(5): 897 -905 .
[5]	Deng Zhiying; Huang Yisheng. Existence of Positive Solutions for a Class of Nonlinear Elliptic Equations[J]. Acta mathematica scientia,Series A, 2008, 28(5): 971 -976 .
[6]	Hou Ruchen;Ye Yu. Ringel-Hall Algebra of A^∞_&infin\|^_type[J]. Acta mathematica scientia,Series A, 2008, 28(6): 1077 -1087 .
[7]	Yang Qing. Upwind Finite Volume Scheme for Semiconductor Device in Three Dimension[J]. Acta mathematica scientia,Series A, 2006, 26(1): 150 -160 .
[8]	Zhu Yujun; He Lianfa. Limit Shadowing Property of Linear Systems[J]. Acta mathematica scientia,Series A, 2007, 27(2): 314 -321 .
[9]	Li Wenming. WEIGHTED INEQUALITIES FOR MULTILINEAR POTENTIAL TYPE OPERATORS[J]. Acta mathematica scientia,Series A, 2006, 26(6): 1144 .
[10]	Liu Xiping; Jia Mei; Ren Rui. On the Existence and Uniqueness of Periodic Solutions to a Type[J]. Acta mathematica scientia,Series A, 2007, 27(1): 37 -044 .

Abstract
References
Related Articles
Metrics
Comments
Recommended

TOP

Existence of Solutions for Fourth Order Boundary Value Problem with p-Laplace at Resonance

PDF (PC)