If we were to paint it red, the white table would cease to exist and the red table would come into existence – the continuity between the two being guaranteed by the table, which was part of the white table and is now part of the green table.
We discuss existence, uniqueness, continuity, boundedness and moment stability of solutions with the help of several Lyapunov-type functions.
The existence of continuity between fascia and muscles that may be anatomically distant from each other is emphasized in the tensegrity principle.
This dreadful journal, almost void of any other content but these passionate assertions and denials, intending to affirm existence and continuity but forever contradicting them, was filled anew each day, and soon mounted to hundreds of almost identical pages.
In this section we formulate auxiliary propositions on the existence and continuity of the Marchaud fractional derivative and its integral representation in terms of the higher-order derivative.
Crandall, Rabinowitz, and Tartar [1] considered the Dirichlet problem to elliptic equation with singular nonlinearity and deduced the existence and continuity of solutions.
Proof of Theorem 2: Using the results of [19], we prove the existence and continuity of the stationary distribution of the Markov chain, {J k }.
Applying the eigenvalue theory and theory of α-concave operator, we establish some new sufficient conditions to guarantee the existence and continuity of positive solutions on a parameter for a second-order impulsive differential equation.
Applying this theorem to various types of Hammerstein integral equations in Banach spaces, it turned out that the hypothesis of existence and continuity of the derivative of the operators related to the studied equation is too restrictive.
Proof of Theorem 3: The existence and continuity of the stationary density Π Θ ( ε 0 ) for every ε0is achieved in a similar way as in the proof of the Theorem 2. The only difference being, ε0 must be added to −M1 in the definition of the set (17).
