In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a co...In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m → 1 or O, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively.展开更多
In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Pal...In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Palais-Smale sequences created from related approximation problems,the existence of infinitely many solutions to the system is established.展开更多
文摘In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m → 1 or O, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively.
基金supported by National Natural Science Foundation of China(Grant Nos.10771219 and 11071092)the PhD Specialized Grant of the Ministry of Education of China(Grant No.20110144110001)
文摘In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Palais-Smale sequences created from related approximation problems,the existence of infinitely many solutions to the system is established.
