Data has to be accessed, signaling a greater need to develop a linking structure and visual way to see updates and interactions in the lifecycle process.
In Section 2, we provide a linking structure for our variational problem (see Theorem 2.2); in Section 3, we verify that the energy functional satisfies the (P.S).
For this matter, first we get two ground states in view of the Nehari procedure, establish a linking structure by the abstract linking theorem on the product space, and then construct the third critical value by the classical minimax principle.
Applying the Nehari procedure and abstract linking theorem on a product space, we give a linking structure for our variational problem, and then, combining with the classical minimax principle, we obtain three nontrivial critical values for the relevant energy functional.
In the following, we will introduce an abstract critical point theorem, which is based on a compactness condition - the ((PS)) condition or the ((Ce)) condition - and on a linking structure.
In this section, we list some preliminaries, including the abstract linking theorem on the product space and the concept of Nehari manifold, and then we give a linking structure, which is useful for constructing the critical value of the functional associated with system (1.1).
The recommendation system thus creates a strong linked structure between similar videos, which influence each other in terms of popularity [95].
