Volume 3, Issue 3-1, June 2015, Page: 19-24
Positive Solutions of a Singular System with Two Point Coupled Boundary Conditions
Naseer Ahmad Asif, Department of Mathematics, School of Science and Technology, University of Management and Technology, Lahore, Pakistan
Received: May 31, 2015;       Accepted: Jun. 1, 2015;       Published: Jun. 15, 2015
DOI: 10.11648/j.ajam.s.2015030301.14      View  3507      Downloads  73
In this paper, we study the existence of positive solutions to a system of nonlinear differential equations subject to two-point coupled boundary conditions. Further, the nonlinearities are allowed to be singular with respect to first order derivatives. An example is included to show the applicability of our result.
Positive Solutions, Coupled System, Singular Ordinary Differential Equations, Coupled Boundary Conditions
To cite this article
Naseer Ahmad Asif, Positive Solutions of a Singular System with Two Point Coupled Boundary Conditions, American Journal of Applied Mathematics. Special Issue: Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015). Vol. 3, No. 3-1, 2015, pp. 19-24. doi: 10.11648/j.ajam.s.2015030301.14
R. P. Agarwal and D. O’Regan, Singular Differential and Integral Equations with Applications, Kluwer Academic Publishers, Dordrecht, 2003.
S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math. 17 (1964) 35-92.
H. Amann, Parabolic evolution equations with nonlinear boundary conditions, in: Nonlinear Functional Analysis and Its Applications, Berkeley, 1983, in: Proc. Sympos. Pure Math., vol. 45, Amer. Math. Soc., Providence, RI, 1986, pp. 17-27.
H. Amann, Parabolic evolution equations and nonlinear boundary conditions, J. Differential Equations 72 (1988) 201-269.
D.G. Aronson, A comparison method for stability analysis of nonlinear parabolic problems, SIAM Rev 20 (1978), 245-264.
N.A. Asif, P.W. Eloe and R.A. Khan, Positive solutions for a system of singular second order nonlocal boundary value problems, Jounnal of the Korean Mathematical Society, 47 (5) (2010) 985 - 1000.
N.A. Asif and R.A. Khan, Positive solutions for a class of coupled system of singular three point boundary value problems, Boundary Value Problems 2009 (2009), Article ID 273063, 18 pages.
N.A. Asif, R.A. Khan and J. Henderson, Existence of positive solutions to a system of singular boundary value problems, Dynamic Systems and Applications, 19 (2010) 395 – 404.
X. Cheng and C. Zhong, Existence of positive solutions for a second-order ordinary differential system, J. Math. Anal. Appl. 312 (2005) 14–23.
R.A. Khan and J.R.L. Webb, Existence of at least three solutions of nonlinear three point boundary value problems with super-quadratic growth, J. Math. Anal. Appl. 328 (2007) 690–698.
A. Leung, A semilinear reactiondiffusion preypredator system with nonlinear coupled boundary conditions: Equilibrium and stability, Indiana Univ. Math. J. 31 (1982) 223-241.
Y. Liu and B. Yan, Multiple solutions of singular boundary value problems for differential systems, J. Math. Anal. Appl. 287 (2003) 540–556.
H. L¨u, H. Yu and Y. Liu, Positive solutions for singular boundary value problems of a coupled system of differential equations, J. Math. Anal. Appl. 302 (2005), 14–29.
F. Ali Mehmeti, Nonlinear Waves in Networks, Math. Res., vol. 80, Akademie-Verlag, Berlin, 1994.
F. Ali Mehmeti, S. Nicaise, Nonlinear interaction problems, Nonlinear Anal. 20 (1993) 27-61.
S. Nicaise, Polygonal Interface Problems, Methoden und Verfahren der Mathematischen Physik, vol. 39, Peter Lang, Frankfurt Main, 1993.
Z. Wei, Positive solution of singular Dirichlet boundary value problems for second order differential equation system, J. Math. Anal. Appl. 328 (2007) 1255–1267.
X. Xian, Existence and multiplicity of positive solutions for multi-parameter three-point differential equations system, J. Math. Anal. Appl. 324 (2006) 472–490.
A. Zettl, Sturm-Liouvillie Theory, Math. Surveys Monogr., vol. 121, Amer. Math. Soc., Providence, RI, 2005.
Browse journals by subject