Existencia de soluciones positivas de problemas con valores en la frontera para ecuaciones diferenciales con impulso acopladas sobre toda la recta con condiciones de frontera mixta.
Resumen
Este artículo está interesado en problemas con valores en la frontera para sistemas diferenciales con impulso sobre la línea recta con operadores diferenciales no lineales. Construyendo un espacio de Banach ponderado y definiendo un operador no lineal, usando el teorema del punto fijo de Schauder y el teorema del punto fijo de Schaefer, se establecen condiciones suficientes para garantizar la existencia de al menos una solución positiva. Se da un ejemplo para ilustrar los principales resultados.
Citas
A. Cabada and J.A. Cid. Heteroclinic solutions for non-autonomous boundary value problems with singular-Laplacian operators, Discrete Contin. Dyn. Syst. 2009, Dynamical Systems, Differential Equations and Applications. 7th AIMS Conference, suppl., 118-122.
A. Calamai. Heteroclinic solutions of boundary value problems on the real line involving singular -Laplacian operators, Journal of Mathematical Analysis and Applications, 378(2011), 667-679.
B. Bianconi and F. Papalini. Non-autonomous boundary value problems on the real line, Discrete and continuous dynamical systems, 15(2006), 759-776.
C. Avramescu and C. Vladimirescu. Existence of Homoclinic solutions to a nonlinear second order ODE, Dynamics of continuous, discrete and impulsive systems, Ser. A, Math Anal. 15(2008), 481-491.
C. Avramescu and C. Vladimirescu. emph{Existence of solutions to second order ordinary differential equations having finite limits at }, Electronic Journal of differential equations, 18(2004), 1-12.
C. Avramescu and C. Vladimirescu. Limits of solutions of a perturbed linear differential equation, Electronic Journal of Qualitative Theory of Differential Equations, 3(2002), 1-11.
C. G. Philos and I. K. Purnaras. A boundary value problem on the whole line to second order nonlinear differential equations, Georgian Mathematical Journal, 17(2010), 241-252.
C. Marcelli and F. Papalini. Heteroclinic connections for fully non-linear non-autonomous second-order differential equations, Journal of Differential Equations, 241(2007), 160-183.
D. O'Regan, B. Yan and R. P. Agarwal. Nonlinear Boundary Value Problems on Semi-Infinite Intervals using Weighted Spaces: An Upper and Lower Solution Approach}, Positivity, 11(1)(2007), 171-189.
D. R. Dunninger and H. Y. Wang. Existence and multiplicity of positive solutions for elliptic systems}. Nonlinear Anal, 29(1997), 1051-1060.
D. R. Dunninger and H. Y. Wang. Multiplicity of positive radial solutions for an elliptic system on an annulus. Nonlinear Anal, 42(2000), 803-811.
E. K. Lee and Y. H. Lee. A global multiplicity result for two-point boundary value problems of p-Laplacian systems. Sci China Math, 53}(4)(2010), 967-984.
F. Y. Deren and N. A. Hamal. Second-order boundary-value problems with integral boundary conditions on the real line, Electronic Journal of Differential Equations, 19(2014), 1-13.
G. Cupini, C. Macelli and F. Papalini. Heteroclinic solutions of boundary value problems on the real line involving general nonlinear differential operators. Differ. Integral Equations, 24(2011), 619-644.
G. Cupini, C. Macelli and F. Papalini. On the solvability of a boundary value problem on the real line, Boundary Value Problem, 2011 (2011): 26.
I. Rachunkova, S. Stanek and M. Tvrdy. Singularities and Laplacians in boundary value problems for nonlinear ordinary differential equations, Handbook of Differential Equations. Ordinary Differential Equations, 3, 606-723, Ed. by A. Canada, P. Drabek, A. Fonde, Elsevier 2006.
K. Deimling. Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
O. J. M. Do, S. Lorca, J. Sanchez, et al. Positive solutions for a class of multiparameter ordinary elliptic systems. J. Math Anal Appl., 332(2007), 1249-1266.
O. J. M. Do, S. Lorca, P. Ubilla. Local superlinearity for elliptic systems involving parameters. J Differential Equations, 211(2005), 1-19.
R.P. Agarwal, Boundary value problems for higher order differential equations, World Scientific, Singapore, 1986.
R.P. Agarwal and D. O'Regan. Infinite interval problems for differential, difference and integral equations. Kluwer Academic Publisher, Dordrecht (2001).
R.P. Agarwal and D. O'Regan. Boundary value problems on the half line modelling phenomena in the theory of colloids. Mathematical Problems in Engineering, 8(2002), 143-150.
R.P. Agarwal and D. O'Regan. Continuous and discrete boundary value problems on the infinite interval: existence theory}, Mathematika, 48(2001), 273-292.
R.P. Agarwal and D. O'Regan. Infinite interval problems modelling phenomena which arise in the theory of plasma and electrical potential theory, Studies in Appl. Math., 111(2003), 339-358.
V. A. Il'in and E. I. Moiseev. Nonlocal boundary-value problem of the second kind for a Sturm-Liouville operator. Differential Equations, 23(1987), 979-987.
V. V. Lakshmikantham, D. D. Bainov and P. S. Simeonov. Theory of Impulsive Differential Equations. World Scientific, Singapore, 1989.
W. Ge. Boundary Value Problems for Ordinary Differential Equations. Science Press, Beijing, 2007.
X. Cheng and Z. Zhang. Positive solutions for a multi-parameter system of second-order ordinary differential equations. Sci. China Math, 54 (5)(2011), 959-972.
Y. H. Lee. A multiplicity result of positive radial solutions for a multi-parameter elliptic system on an exterior domain. Nonlinear Anal, 45(2001), 597-611.
Y. H. Lee. Multiplicity of positive radial solutions for multi-parameter semilinear elliptic systems on an annulus. J. Differential Equations, 174(2001), 420-441.
Y. Liu. Solvability of boundary value problems for singular quasi-Laplacian differential equations on the whole line. Mathematical Models and Analysis, 17(2012), 423-446.
Y. Liu. Existence of solutions of boundary value problems for coupled singular differential equations on whole lines with impulses. Mediterr. J. Math. DOI 10.1007/s00009-014-0422-1, to appear.
Y. Wang and W. Ge. Existence of triple positive solutions for multi-point boundary value problems with a one dimensional p-Laplacian. Computers and Mathematics with Applications, 54(2007), 793-807.