Back
 JAMP  Vol.3 No.4 , April 2015
The Existence and Multiplicity of Solutions for Singular Boundary Value Systems with p-Laplacian
Abstract: This paper presents sufficient conditions for the existence of positive solutions for the fourth-order boundary value problem system with p-Laplacian operator. The existence of single or multiple positive solutions for the system is showed through the fixed point index theory in cones under some assumptions.
Cite this paper: Cai, Z. (2015) The Existence and Multiplicity of Solutions for Singular Boundary Value Systems with p-Laplacian. Journal of Applied Mathematics and Physics, 3, 411-416. doi: 10.4236/jamp.2015.34052.
References

[1]   Korman, P. (2004) Uniqueness and Exact Multiplicity of Solutions for a Class of Fourth-Order Semilinear Problems. Proceedings of the Royal Society of Edinburgh Section A—Mathematics, A134, 179-190. http://dx.doi.org/10.1017/S0308210500003140

[2]   Ma, R. and Wu, H. (2002) Positive Solutions of a Fourth-Order Two-Point Boundary Value Problem. Acta Mathematica Sinica, A22, 244-249. (In Chinese)

[3]   Yao, Q. (2004) Positive Solutions for Eigenvalue Problems of Fourth-Order Elastic Beam Equations. Applied Mathematics Letters, 17, 237-243. http://dx.doi.org/10.1016/S0893-9659(04)90037-7

[4]   Ma, R.Y. and Wang, H.Y. (1995) On the Existence of Positive Solutions of Fourth-Order Ordinary Differential Equations. Applicable Analysis, 59, 225-231. http://dx.doi.org/10.1080/00036819508840401

[5]   Sun, W.P. and Ge, W.G. The Existence of Positive Solutions for a Class of Nonlinear Boundary Value Problems. Acta Mathematica Sinica, 44, 577-580. (In Chinese)

[6]   Agarwal, R.P., O’Regan, D. and Wong, P.J. (2000) Positive Solutions of Differential. Difference and Integral Equations. Springer-Verlag, Singapore.

[7]   Ma, R.Y. (2000) Multiple Nonnegative Solutions of Second-Order Systems of Boundary Value Problems. Nonlinear Analysis, 42, 1003-1010. http://dx.doi.org/10.1016/S0362-546X(99)00152-2

[8]   Ni, X.H. and Ge, W.G. (2005) Existence of Positive Solutions for One-Dimensional p-Laplacian Coupled Boundary Value Problem. J. Math. Rese. Expo., 25, 489-494. (In Chinese)

[9]   Guo, D.J. (2000) Nonlinear Functional Analysis. Science and Technology, Jinan.

 
 
Top