Abstract
By using the classical fixed point theorem for operators on a cone, in this paper, some results of single and multiple positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. It is worth noticing that the nonlinearity f and the pulse function in this paper are not positive.
Highlights
1 Introduction The theory of dynamic equations on time scales has been a new important mathematical branch [ – ] since it was initiated by Hilger [ ]
The boundary value problems of impulsive dynamic equations on time scales have received considerable attention [ – ] since the theory of impulsive differential equations is much richer than the corresponding theory of differential equations without impulse effects [ – ]
The main tool used in this paper is the classical fixed point theorem for operators on a cone
Summary
The theory of dynamic equations on time scales has been a new important mathematical branch [ – ] since it was initiated by Hilger [ ]. In [ ], by using the Guo-Krasnoselskii fixed point theorem, when the nonlinearity f and the pulse function are positive, Wang considered the existence of one or two positive solutions to the following PBVPs of impulsive dynamic equations on time scales:. In [ ], by using the Schaefer fixed point theorem, Wang and Weng obtained the existence of at least one solution to the problem ). Motivated by the results mentioned above, in this paper, we shall obtain the existence of single and multiplicity positive solutions to the problem The main tool used in this paper is the classical fixed point theorem for operators on a cone.
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