Sentence examples for continuation and uniqueness from inspiring English sources

The existence, continuation and uniqueness of Filippov's solution to the system are, therefore, investigated.

In the present paper, we use the method of continuation to obtain an existence and uniqueness result for a kind of FBSDEs with Poisson jumps under some monotonicity conditions.

Thus Mawhin's continuation theorem can be used to study the existence and uniqueness of periodic solutions to equation (1.9) and equation (1.10).

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.

Using a generalized Mawhin continuation theorem, we obtain some sufficient conditions which guarantee the existence and uniqueness of periodic solutions for two types of prescribed mean curvature p-Laplacian equations.

By using the method of continuation, Wu [7] weakens the monotonicity conditions and obtains the existence and uniqueness of the solutions to two-point boundary value problems for ODEs (1.1) and also the corresponding comparison theorem.

By applying Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence and uniqueness of periodic solutions for the above equation.

Using the method of continuation, the Itô product rule of semimartingales, and the fixed point principle, based on the theory of BSDEs driven by a continuous-time finite-state Markov chain, we obtain existence and uniqueness results of the FBSDEs on a Markov chain.

By using the Manásevich-Mawhin continuation theorem and some analysis skills, we establish some sufficient condition for the existence and uniqueness of positive T-periodic solutions for a generalized Rayleigh type ϕ-Laplacian operator equation.

(1.4) By using the Manásevich-Mawhin continuation theorem and some analysis techniques, the authors established a sufficient condition for the existence and uniqueness of positive periodic solutions for (1.4).

The existence and uniqueness of sign-changing solutions for the problems are obtained by Leray-Schauder continuation theorem and analytical technique.