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In Section 3 the extended Rapcs´ ak system with curvature condition is considered in the n-dimensional generic case, when the eigenvalues of the Jacobi curvature tensor Φ are
We show that a discrete fixed point theorem of Eilenberg is equivalent to the restriction of the contraction principle to the class of non-Archimedean bounded metric spaces.. We
In particular, we show that the strong convergence implies the weak convergence and disprove the converse through a counter-example, by invoking an analogue of Parseval’s identity
We prove Levy’s Theorem for a new class of functions taking values from a dual space and we obtain almost sure strong convergence of martingales and mils satisfying various
(4) The basin of attraction for each exponential attractor is the entire phase space, and in demonstrating this result we see that the semigroup of solution operators also admits
In section 3 all mathematical notations are stated and global in time existence results are established in the two following cases: the confined case with sharp-diffuse
Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A
We construct a sequence of a Newton-linearized problems and we show that the sequence of weak solutions converges towards the solution of the nonlinear one in a quadratic way.. In