Sentence examples for by applying the continuation from inspiring English sources
By applying the continuation theorems, Gaines and Mawhin proved that the Rayleigh equation can support periodic solutions.
By applying the continuation theorem and some analytic techniques, we shall establish several new criteria for the existence of positive periodic solutions for the considered problem.
The sufficient conditions for the existence of solutions of coupled fractional differential equations are obtained by applying the Mawhin continuation theorem.
In Sect. 2 we give a prior estimate and obtain the proof of Theorem 1.1 by applying the homotopy continuation method.
By applying the Manásevich-Mawhin continuation theorem, the authors proved that equation (1.2) has at least one positive T-periodic solution.
By applying the Manásevich-Mawhin continuation theorem, we establish some sufficient conditions for the existence and uniqueness of positive periodic solutions for the Liénard type ϕ-Laplacian operator equation.
In [22, 24 45], the authors investigated the existence and exponential stability of anti-periodic solutions for some neural networks by applying the differential inequality techniques, the continuation theorem of coincidence degree theory, the contraction mapping principle, and the Lyapunov functional method, respectively.
The equations of motion are developed by applying the principle of virtual work and are solved by a continuation method.
The equations of motion are developed by applying the principle of virtual work and are solved by a continuation method, 1 3 and 1 5 internal resonances are discovered and their consequences are discussed.
The climate scenarios were (i) a continuation of the historical climate of 1975 2007; (ii) a continuation of the more recent climate of 1997 2007 until 2030; and (iii v) three climate scenarios derived by applying the GCM projected climate under three global warming scenarios of 0.7, 1.0 and 1.3 °C by 2030.
The controller design directly employs the nonlinear model exploited based on mean-value modeling principle of engine systems without any linearizing reformation, and the online optimization is achieved by applying the Continuation/GMRES (generalized minimum residual) approach.
