Under certain nonlinear growth conditions of the nonlinearity, we obtain a new result on the existence of solutions by using the continuation theorem of coincidence degree theory.
By using the continuation theorem of coincidence degree theory, we study the existence of solutions of Duffing type fractional differential equations with a p-Laplacian operator.
By using the continuation theorem of coincidence degree theory and the method of Schrödingerean Lyapunov functional, some sufficient conditions were obtained.
(1.2) Using the continuation theorem of coincidence degree theory, they obtained the existence of periodic solutions for (1.2).
By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is obtained.
In [16], using the continuation theorem of Ge and Ren [11], the author investigated the existence of solutions for the problem left { textstylebegin{array}l} (varphi_{p} u'))'+f t,u,u')=0,quad 0< t< +infty, u(0)=0, qquadvarphi_{p} u'(+infty))=sum_{i=1}^{n}alpha_{i}varphi _{p} u'(xi_{i})) end{array}displaystyle right.
By using the continuation theorem of coincidence degree theory, we obtain a new result on the existence of solutions for the considered problem.
By using the continuation theorem of Mawhin's coincidence degree theory and some inequality techniques, some new sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of neural networks with variable coefficients and time-varying delays.
By using the continuation theorem of Mawhin's coincidence degree theory and Gronwall's inequality, some new sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of cellular neural networks with periodic coefficients and delays.
By using the continuation theorem of Mawhins coincidence degree theory and constructing a suitable Lyapunov function, some new sufficient conditions are obtained ensuring existence and global asymptotical stability of periodic solution of cellular neural networks with periodic coefficients and delays, which do not require the activation functions to be differentiable and monotone nondecreasing.
