This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further ext...This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.展开更多
We construct a loop algebra 3 , then a new 4×4 isospectral problem is presented. By Tu scheme, the generalized coupled mKdV equation hierarchy is derived. Based on an expanding loop algebra F3 of the loop algebra...We construct a loop algebra 3 , then a new 4×4 isospectral problem is presented. By Tu scheme, the generalized coupled mKdV equation hierarchy is derived. Based on an expanding loop algebra F3 of the loop algebra 3 , the integrable couplings of the generalized coupled mKdV hierarchy is solved. Finally, the Hamiltonian structures of the integrable couplings of the generalized coupled mKdV hierarchy is obtained by the quadratic-form identity.展开更多
In this paper, we consider the existence of positive solutions of the semlinear elliptic boundary value problem with convex and concave nonlinearities, the results obtained improve and generalize some known results.
In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of non-autonomous nonlinear neutral difference equation. We extend the results in [1].
This paper discusses the oscillation of second-order nonlinear differential equations with impulses. Sufficient conditions for all solutions of the equation to be oscillated are obtained.
In this paper, we consider a p（x）-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our app...In this paper, we consider a p（x）-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our approach relies on the theory of variable exponent Sobolev space.展开更多
We study the existence of solutions to a class of p(x)-Laplacian equations involving singular Hardy terms for nonlinear terms of the type f(x, t) = ±(-λ|t|m(x)-2t +|t|q(x)-2t). First we show the existence of inf...We study the existence of solutions to a class of p(x)-Laplacian equations involving singular Hardy terms for nonlinear terms of the type f(x, t) = ±(-λ|t|m(x)-2t +|t|q(x)-2t). First we show the existence of infinitely many weak solutions for anyλ 】 0, and next prove that if λ is large enough then there exists a nontrivial weak solution. Our approach relies on direct variational methods and the theory of variable exponent Lebesgue-Sobolev spaces.展开更多
文摘This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.
基金supported by the National Natural Science Foundation of China (Grant Nos.11271008, 61072147, 1071159)the Shanghai Leading Academic Discipline Project (No.J50101)+2 种基金the Shanghai Univ. Leading Academic Discipline Project (A.13-0101-12-004)the Youth Foundation of Zhoukou Normal University (2012QNB09)Science and Technology Project of Henan Province (132400410582)
文摘We construct a loop algebra 3 , then a new 4×4 isospectral problem is presented. By Tu scheme, the generalized coupled mKdV equation hierarchy is derived. Based on an expanding loop algebra F3 of the loop algebra 3 , the integrable couplings of the generalized coupled mKdV hierarchy is solved. Finally, the Hamiltonian structures of the integrable couplings of the generalized coupled mKdV hierarchy is obtained by the quadratic-form identity.
文摘In this paper, we consider the existence of positive solutions of the semlinear elliptic boundary value problem with convex and concave nonlinearities, the results obtained improve and generalize some known results.
文摘In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of non-autonomous nonlinear neutral difference equation. We extend the results in [1].
基金the Foundation of Binzhou University (BZXYQMG200622)the Foundation of Educational Department of Shandong Province (J07WH01)
文摘This paper discusses the oscillation of second-order nonlinear differential equations with impulses. Sufficient conditions for all solutions of the equation to be oscillated are obtained.
基金supported in part by the NNSF of China(Grant No.11101145)Research Initiation Project for Highlevel Talents(201031)of North China University of Water Resources and Electric Power
文摘In this paper, we consider a p（x）-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our approach relies on the theory of variable exponent Sobolev space.
基金supported by Educational Commission of Henan Province(No.14A110013)
文摘We study the existence of solutions to a class of p(x)-Laplacian equations involving singular Hardy terms for nonlinear terms of the type f(x, t) = ±(-λ|t|m(x)-2t +|t|q(x)-2t). First we show the existence of infinitely many weak solutions for anyλ 】 0, and next prove that if λ is large enough then there exists a nontrivial weak solution. Our approach relies on direct variational methods and the theory of variable exponent Lebesgue-Sobolev spaces.
