Sentence examples for existence is obtained from inspiring English sources

Based on these spaces and the coincidence degree theory, a 2m-point boundary value problem for a coupled system of impulsive fractional differential equations at resonance is considered, and the new criterion on existence is obtained.

When the viscosity coefficient (mu(rho)) is density-dependent and (lambda(rho)) is a positive constant, the global existence was obtained in [26].

Five of the nine QTL detected with the original F2 population were confirmed and fine-mapped with the AIL, while for the remaining four, only suggestive evidence of their existence was obtained.

In our algorithm, the set of all morphisms, or a proof of non-existence, are obtained by backtracking.

An existence result is obtained with the use of the coincidence degree theory.

Under proper conditions on V, f, g, and K, the existence result is obtained by using variational methods.

A new existence result is obtained by making use of a nonlinear alternative for contractive maps and is well illustrated with the aid of an example.

Under certain nonlinear growth conditions of the nonlinearity, a new existence result is obtained by using the Schaefer fixed point theorem.

Under certain nonlinear growth conditions of the nonlinearity, a new existence result is obtained by using Schaefer's fixed point theorem.

Then the existence result is obtained via constructing a minimax level within this range and the mountain pass lemma due to Ambrosetti and Rabinowitz (see also [15]).

In Section 3, some sufficient conditions for the existence of solutions for PBVP (1.2) are established, and a new result on the existence of solutions is obtained.