Sentence examples for by utilizing the fixed from inspiring English sources
They dealt with many boundary conditions given in the literature in a unified way by utilizing the fixed point index theory in cones.
Finally, by utilizing the fixed point index theory, we establish the multiplicity of positive solutions for the case 0 < λ < λ ∗.
By utilizing the fixed point theorems, we derive many existence results concerning the mild solutions for problem (2) under different assumptions on the nonlinear term and nonlocal term.
Theorems on the existence of positive solutions are obtained by utilizing the fixed point theorem of cone expansion and compression type.
In this section, we first formulate and prove sufficient conditions for the existence and uniqueness of a mild solution of system (1)–(3) by utilizing the fixed-point theory.
In particular, Sakthivel et al. [1, 46] analyzed the existence and approximate controllability of fractional stochastic integro-differential equations with infinite delay by utilizing the Krasnoselskii fixed point theorem.
The purpose of this paper is to establish the criteria of the existence of a positive solution to the problem (1.1) by utilizing the Krasnosel'skii fixed point theorem, even if some of the α i coefficients are negative.
Very recently, Balasubramaniam and Tamilalagan [36] analyzed a new set of sufficient conditions for the approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay in Hilbert spaces by utilizing the Bohnenblust-Karlin fixed point theorem, Mainardi's function, operator semigroups, and fractional calculus.
As discussed above, we determine the abundance of mutants at the time of therapy initiation by utilizing the deterministic fix-point as starting condition for our simulations.
By utilizing the same method, the MWCNT was fixed.
