They obtain various existence results applying coincidence degree theory and the method of upper and lower solutions.
By applying coincidence degree theory, they obtained sufficient conditions for the existence of periodic solutions to a Rayleigh neutral differential equation.
For this problem, we focus on an important class of resonant problems when L is a Fredholm operator with zero-index, as a prerequisite for applying coincidence degree theory [8].
By applying coincidence degree theorem of Mawhin to integral boundary value problems on time scales at resonance, this paper will establish some sufficient conditions for the existence of at least one solution to BVPs (1.1).
In Section 2, we introduce some technical tools and present all the auxiliary results; in Section 3, by applying coincidence degree theory and some new inequalities, we obtain sufficient conditions for the existence of positive periodic solutions for (1.4), an example is also given to illustrate our results.
Now, we are ready to apply the coincidence degree theorem of Mawhin to give the sufficient conditions for the existence of at least one solution to problem (1.1).
In this paper, we consider a system of integral equations and apply the coincidence and common fixed point theorems for four mappings satisfying a -weakly contractive condition in ordered metric spaces to prove the existence of a common solution to integral equations.
A more appropriate approach would be to estimate K α coefficients representing the random variability from replicate arrays and apply the coincidence test to the initial sets of genes lying outside the intervals defined by these values.
By applying the coincidence degree theorem due to Mawhin, we show the existence of at least one solution to the nonlinear second-order differential equation.
By considering a suitably modified nonlinearity and applying the coincidence degree method of Mawhin [21], the existence of multiple solutions for the problem (1.1 - 1.2 1.1 - 1.2.
