By use of the existence theorem of three critical points given by Ricceri [13], they obtained sufficient conditions for the existence of three solutions to the discussed system, when the parameter λ is defined in a certain interval ([0,delta]).
The assumption of continuity is often used in the existence theorems of fixed points [6, 9 14].
We also give an example to show that the family above is not necessary to be commuting, and in contrast that the commutativity assumption is often used in the existence theorems of common fixed points [9, 10, 13, 15, 16].
Finally, by using the conditions of the existence theorem of the solutions to (SVQEP) (see [1]), we obtain sufficient conditions of the well-posedness for (SVQEP).
In this paper, for the first time, the existence theorem from [12] is used for studying the boundary value problem with the nonlinearity f depending also on the derivative.
Now we will use the Banach fixed point theorem to prove the existence theorem for (2.1).
By using fixed point theory and set-valued analysis, we establish the existence theorem of equilibrium point.
By using some fixed point theorems, the existence theorems of mild solutions are obtained, our results are also more general than some well-known results.
In this paper, by constructing completely different auxiliary functions with those in [21 23] and technically using maximum principles, we obtain some existence theorems of a global solution, an upper estimate of the global solution, the existence theorems of a blow-up solution, an upper bound of 'blow-up time', and an upper estimates of 'blow-up rate'.
Analytic conditions for existence and stability of synchronization regimes, and analytic expressions for their stable amplitudes and period corrections are derived using the Poincaré theorem on existence of periodic solutions in autonomous quasi-linear systems.
