Abstract： In this paper, we are interested in the existence and multiplicity results ofnontrivial solutions to nonhomogeneous singularelliptic systems with critical C-K-N exponent（λ1,λ2）.With the help of the Neha...Abstract： In this paper, we are interested in the existence and multiplicity results ofnontrivial solutions to nonhomogeneous singularelliptic systems with critical C-K-N exponent（λ1,λ2）.With the help of the Nehari manifold and under sufficient conditions on the parameters λ1 and λ2, we prove some existence results.展开更多
The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications ...The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications have sprung up recently.The prediction of wave competitions is also very important and quite useful in these fields.This paper considers the behaviors of wave competitions in simple,inhomogeneous media which is modeled by Brusselator equations.We present a simple rule to judge the results of wave competitions utilizing the dispersion relation curves and the waves coming from different wave sources.Moreover,this rule can also be used to predict the results of wave propagation.It provides methods of obtaining the desired waves with given frequencies in inhomogeneous media.All our results are concluded and verified by computer simulations.展开更多
The problem of an ellipsoidal inhomogeneity embedded in an infinitely extended elastic medium with sliding interfaces is investigated. An exact solution is presented for such an inhomogeneous system that is subject to...The problem of an ellipsoidal inhomogeneity embedded in an infinitely extended elastic medium with sliding interfaces is investigated. An exact solution is presented for such an inhomogeneous system that is subject to remote uniform shearing stress. Both the elastic inclusion and matrix are considered isotropic with a separate elastic modulus. Based on Lur’e’s approach to solving ellipsoidal cavity problems through Lamé functions, several harmonic functions are introduced for Papkovich-Neuber displacement potentials. The displacement fields inside and outside the ellipsoidal inclusion are obtained explicitly, and the stress field in the whole domain is consequently determined.展开更多
文摘Abstract： In this paper, we are interested in the existence and multiplicity results ofnontrivial solutions to nonhomogeneous singularelliptic systems with critical C-K-N exponent（λ1,λ2）.With the help of the Nehari manifold and under sufficient conditions on the parameters λ1 and λ2, we prove some existence results.
基金Supported by National Natural Science Foundation of China under Grant Nos.11105051,11104071,11247272Fundamental Research Funds for Central Universities,Beijing Higher Education Elite Young Teacher ProjectYouth Scholars Program of Beijing Normal University
文摘The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications have sprung up recently.The prediction of wave competitions is also very important and quite useful in these fields.This paper considers the behaviors of wave competitions in simple,inhomogeneous media which is modeled by Brusselator equations.We present a simple rule to judge the results of wave competitions utilizing the dispersion relation curves and the waves coming from different wave sources.Moreover,this rule can also be used to predict the results of wave propagation.It provides methods of obtaining the desired waves with given frequencies in inhomogeneous media.All our results are concluded and verified by computer simulations.
基金supported by the National Natural Science Foundation of China(Grant No.11102022)
文摘The problem of an ellipsoidal inhomogeneity embedded in an infinitely extended elastic medium with sliding interfaces is investigated. An exact solution is presented for such an inhomogeneous system that is subject to remote uniform shearing stress. Both the elastic inclusion and matrix are considered isotropic with a separate elastic modulus. Based on Lur’e’s approach to solving ellipsoidal cavity problems through Lamé functions, several harmonic functions are introduced for Papkovich-Neuber displacement potentials. The displacement fields inside and outside the ellipsoidal inclusion are obtained explicitly, and the stress field in the whole domain is consequently determined.
