In this paper,we prove the existence of sign-changing solution for nonlinear elliptic problem:-Δu=λh(x)u+a(x)f(u),by using of linking methods,where a(x) changes sign,h(x)>0 and λ>0.

By using critical theory and linking methods,we give two sets of hypotheses which guarantee the existence of non-constant solutions.

By using the linking theorem on single space and on product space developed by Zhao et al, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for nonlinear difference equations and systems.

Under some nature conditions,it is proved that the conditions of Brezis-Nirenberg theorem and the conditions of link theorem given by Du are equivalent.

When annular rotary jet injects across the main flow, its curved shape and the process of dispersing the upper corners gas accumulation of U shaped working face are analyzed.

Based on the basic theory and related research achievements of jet, the entrainment and dilution effects of rotary jet on gas with high concentration were analyzed, and its deforming and curving characteristics during crosscutting the main airflow of coal faces was discussed.

Infrared control system with learning function in ambient intelligence;

Architecture of the smart home network in ambient intelligence;

Design of Cell Phone Based House-Hold Surveillance System in Ambient Intelligence Environment;

Rabinowitz s linking theorem in critical point theory,the existence of T-periodic solution to second-order Hamiltonian system under the superquadratic condition was demonstrated.

Via Linking Theorem and some estimates about the solutions,we consider a semilinear elliptic problem:-△u-μ/(|x|2)u=k(x)|u|2*-2u+λu,u∈H01(Ω),when k(x) satisfies some conditions,we can prove the existence of a nontrivial solution.

Using the Linking theorem and delicate estimates to study the existence of a nontrivial solution for the following semilinear elliptic equation with singularity at zero:-Δu+k(x)｜x｜2u=｜u｜2*-2u,u∈D1,20(Ω), where k(x) satisfies some conditions and 2*=2N/(N-2)(N≥3).