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Positive solutions for a nonlinear differential equation on a measure chain. (English) Zbl 0963.34020
Summary: The authors are concerned with proving the existence of positive solutions to general two-point boundary value problems for the nonlinear equation $$Lx(t):= -[r(t) x^\Delta(t)]^\Delta= f(t, x(t)).$$ They use fixed-point theorems concerning cones in a Banach space. Important results concerning Green functions for general two-point boundary value problems for $$Lx(t):= -[r(t) x^\Delta(t)]^\Delta= 0$$ are given.

34B18Positive solutions of nonlinear boundary value problems for ODE
34A34Nonlinear ODE and systems, general
Full Text: DOI
[1] Hilger, S.: Analysis on measure chains--A unified approach to continuous and discrete calculus. Results in mathematics 18, 18-56 (1990) · Zbl 0722.39001
[2] Agarwal, R.; Bohner, M.: Basic calculus on time scales and some of its applications. Results in mathematics 35, 3-22 (1999) · Zbl 0927.39003
[3] Agarwal, R.; Bohner, M.: Quadratic functional for second order matrix equations on time scales. Nonlinear analysis 33, 675-692 (1998) · Zbl 0938.49001
[4] Agarwal, R.; Bohner, M.; Wong, P.: Sturm-Liouville eigenvalue problems on time scales. Applied mathematics and computation 99, 153-166 (1999) · Zbl 0938.34015
[5] Erbe, L.; Hilger, S.: Sturmian theory on measure chains. Differential equations and dynamical systems 1, 223-246 (1993) · Zbl 0868.39007
[6] Erbe, L. H.; Peterson, A.: Green’s functions and comparison theorems for differential equations on measure chains. Dynamics of continuous, discrete and impulsive systems 6, 121-137 (1999) · Zbl 0938.34027
[7] Ahlbrandt, C.; Peterson, A.: Discrete Hamiltonian systems: difference equations, continued fractions, and Riccati equations. (1996) · Zbl 0860.39001
[8] Kelley, W.; Peterson, A.: Difference equations: an introduction with applications. (1991) · Zbl 0733.39001
[9] Aulbach, B.; Hilger, S.: Linear dynamic processes with inhomogeneous time scale. Nonlinear dynamics and quantum dynamical systems (1990) · Zbl 0719.34088
[10] Deimling, K.: Nonlinear functional analysis. (1985) · Zbl 0559.47040
[11] Krasnoselskii, M.: Positive solutions of operator equations. (1964)
[12] Erbe, L. H.; Hu, S.; Wang, H.: Multiple positive solutions of some boundary value problems. Journal of mathematical analysis and applications 184, 640-648 (1994) · Zbl 0805.34021
[13] Erbe, L. H.; Tang, M.: Positive radial solutions to nonlinear boundary value problems for semilinear elliptic problems. Differential equations and control theory, 45-53 (1995) · Zbl 0845.35033
[14] Erbe, L. H.; Tang, M.: Existence and multiplicity of positive solutions to nonlinear boundary value problems. Differential equations and dynamical systems 4, 313-320 (1996) · Zbl 0868.35035
[15] Wang, H.: On the existence of positive solutions for semilinear elliptic equations in the annulus. Journal of differential equations 109, 1-7 (1994) · Zbl 0798.34030
[16] Kaymakcalan, B.; Laksmikantham, V.; Sivasundaram, S.: Dynamical systems on measure chains. (1996) · Zbl 0869.34039