It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. ...It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for展开更多
In this paper, we prove the existence of a positive solution and a negative solution for a class of second order difference equations with dependence on the first order difference. Our proofs are based on the Mountain...In this paper, we prove the existence of a positive solution and a negative solution for a class of second order difference equations with dependence on the first order difference. Our proofs are based on the Mountain Pass Lemma and iterative methods.展开更多
基金This paper is supported by the National Foundations.
文摘It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for
基金Foundation item： the National Natural Science Foundation of China （No. 60574075） Innovation Program of Shanghai Municipal Education Commissiion （No. 08YZ93） and Shanghai Leading Academic Discipline Project （No. S30501）.
文摘In this paper, we prove the existence of a positive solution and a negative solution for a class of second order difference equations with dependence on the first order difference. Our proofs are based on the Mountain Pass Lemma and iterative methods.
