To be precise, the existence of a smallest positive solution, a greatest negative solution, as well as a sign-changing solution of problem (1.1) is proved by using variational and topological tools, for example, critical point theory, Mountain-Pass Theorem, and the Second Deformation Lemma.
Not only is the origin of speech disputed among experts, but the precise reasons for the existence of the numerous languages of the world are also far from clear.
A third feature is the maintenance of detailed official records and the existence of precise paper procedures through which the personnel of the system communicate with each other and with the public.
We have no need in this case to resolve the existence or precise contours of the major rules (or major questions) doctrine described by our colleagues.
In this way he hopes to avoid the hard questions about our ability to summon empirical verification of their existence or precise character.
The existence of precise temporal relations in sequences of spike intervals, referred to as 'spatiotemporal patterns', is suggested by brain theories that emphasize the role of temporal coding.
In this section, we give precise conditions for the existence of a Hopfield network on (binom{v}{2}) nodes that stores all k-cliques for k in an interval ([m,M]), (m leq M leq v).
To be precise, we prove the existence of weak solutions for the quasilinear Choquard equation (P) under the Cerami condition, as a weak version of the Palais Smale condition.
To be precise, we establish an existence result of at least one solution, Theorem 3.1, which is based on Theorem 2.1, and we point out some consequences, Theorems 3.2, 3.3 and 3.4.
It is known that the Nielsen number gives more precise information about the existence of fixed points than the Lefschetz number, but its computation is in general very difficult.
