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Twin solutions of boundary value problems for differential equations on measure chains. (English) Zbl 1134.39301

Summary: A new twin fixed point theorem is applied to obtain the existence of at least two positive solutions for the right focal boundary value problem on a measure chain.

MSC:

39A10 Additive difference equations
34B99 Boundary value problems for ordinary differential equations
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[1] Agarwal, R.P., Focal boundary value problems for differential and difference equation, (1998), Kluwer Dordrecht
[2] Agarwal, R.P.; Bohner, M., Basic calculus on time scales and some of its applications, Results math., 35, 3-22, (1999) · Zbl 0927.39003
[3] Agarwal, R.P.; O’Regan, D.; Wong, P.J.Y., Positive solutions of differential, difference and integral equations, (1999), Kluwer Dordrecht · Zbl 0923.39002
[4] E. Akin, Boundary value problems for a differential equation on a measure chain, PanAmer. Math. J., in press. · Zbl 0973.39010
[5] F.M. Atici, G.Sh. Guseinov, On a Green’s function and positive solutions for boundary value problems on time scales, preprint. · Zbl 1007.34025
[6] B. Aulbach, S. Hilger, Linear dynamic processes with inhomogeneous time scale, in: Nonlinear Dynamics and Quantum Dynamical Systems, Mathematical Research, Vol. 59, Akademie Verlag, Berlin, 1990. · Zbl 0719.34088
[7] R.I. Avery, C.J. Chyan, J. Henderson, Twin solutions of boundary value problems for ordinary differential equations and finite difference equations, Comput. Math. Appl., in press. · Zbl 1006.34022
[8] Avery, R.I.; Henderson, J., Three symmetric positive solutions for a second order boundary value problem, Appl. math. lett., 13, 1-7, (2000) · Zbl 0961.34014
[9] Avery, R.I.; Henderson, J., Two positive fixed points of nonlinear operators on ordered Banach spaces, Comm. appl. nonlinear anal., 8, 27-36, (2001) · Zbl 1014.47025
[10] R.I. Avery, A.C. Peterson, Three positive fixed points of nonlinear operators on ordered Banach spaces, preprint. · Zbl 1005.47051
[11] Avery, R.I.; Peterson, A.C., Multiple positive solutions of a discrete second order conjugate problem, Panamer. math. J., 8, 39-55, (1998)
[12] Chyan, C.J.; Henderson, J., Eigenvalue problems for nonlinear differential equations on a measure chain, J. math. anal. appl., 245, 547-559, (2000) · Zbl 0953.34068
[13] Chyan, C.J.; Henderson, J., Multiple solutions for 2mth order sturm – liouville boundary value problems, Comput. math. appl., 40, 231-237, (2000) · Zbl 0958.34018
[14] Chyan, C.J.; Lo, H.C.; Henderson, J., Positive solutions in an annulus for nonlinear differential equations on a measure chain, Tamkang J. math., 30, 231-240, (1999) · Zbl 0995.34017
[15] Davis, J.M.; Erbe, L.H.; Henderson, J., Multiplicity of positive solutions for higher order sturm – liouville problems rocky mountain, J. math., 31, 169-184, (2001) · Zbl 0989.34012
[16] Eloe, P.W.; Henderson, J., Twin solutions for nonlinear multipoint conjugate boundary value problems, Dynamics contin. discrete impuls. systems, 5, 283-293, (1999) · Zbl 0942.34016
[17] Eloe, P.W.; Henderson, J.; Kaufmann, E., Multiple positive solutions for difference equations, J. difference equations appl., 3, 219-229, (1998) · Zbl 1005.39502
[18] Erbe, L.H.; Peterson, A., Green’s functions and comparison theorems for differential equations on measure chains, Dynamics contin. discrete impuls. systems, 6, 121-137, (1999) · Zbl 0938.34027
[19] Erbe, L.H.; Peterson, A., Positive solutions for a nonlinear differential equation on a measure chain, Math. comput. modelling, 32, 571-585, (2000) · Zbl 0963.34020
[20] Henderson, J., Multiple solutions for 2mth order sturm – liouville boundary value problems on a measure chain, J. difference equations appl., 6, 417-429, (2000) · Zbl 0965.39008
[21] Henderson, J.; Thompson, H.B., Multiple symmetric positive solutions for a second order boundary value problem, Proc. amer. math. soc., 128, 2373-2379, (2000) · Zbl 0949.34016
[22] Henderson, J.; Thompson, H.B., Existence of multiple solutions for second order boundary value problems, J. differential equations, 166, 443-454, (2000) · Zbl 1013.34017
[23] Hilger, S., Analysis on a measure chain—a unified approach to continuous and discrete calculus, Resultate math., 18, 18-56, (1990) · Zbl 0722.39001
[24] Kaufmann, E., Multiple positive solutions for higher order boundary value problems, Rocky mountain J. math., 28, 1017-1028, (1998) · Zbl 0930.34010
[25] Kaymakcalan, B.; Lakshmikantham, V.; Sivasundaram, S., Dynamical systems on measure chains, (1996), Kluwer Boston · Zbl 0869.34039
[26] Krasnosel’skii, M.A., Positive solutions of operator equations, (1964), Noordhoff, Groningen The Netherlands
[27] Merdivenci, F., Two positive solutions for a boundary value problem for difference equations, J. difference equations appl., 1, 262-270, (1995) · Zbl 0854.39001
[28] Wong, P.J.Y.; Agarwal, R.P., Eigenvalue intervals and double positive solutions of certain discrete boundary value problems, Comm. appl. anal., 3, 189-217, (1999) · Zbl 0923.39002
[29] Wong, P.J.Y.; Agarwal, R.P., Existence of multiple solutions of discrete two-point right focal boundary value problems, J. difference eqs. appl., 5, 517-540, (1999) · Zbl 0964.39004
[30] Zeidler, E., Nonlinear functional analysis and its applications I: fixed-point theorems, (1993), Springer New York
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