Publications (15)15.86 Total impact
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ABSTRACT: We give several sufficient conditions under which the firstorder nonlinear Hamiltonian system x' (t) = alpha (t)x (t)+f(t, y(t)), y'(t) = g (t,x (t))alpha(t)y(t) has no solution (x (t), y(t)) satisfying condition 0 <integral(+infinity)(infinity)[vertical bar x(t)vertical bar(nu)+(1+beta(t))vertical bar y(t)vertical bar(mu)]dt < +infinity, where mu,nu > 1 and (1/mu) + (1/nu) = 1, 0 <= xf (t, x) <= beta(t)vertical bar x vertical bar(mu), xg(t, x) <= gamma(0)(t)vertical bar x vertical bar(nu), beta(t), gamma(0) (t) >= 0, and alpha (t) are locally Lebesgue integrable realvalued functions defined on R.  [Show abstract] [Hide abstract]
ABSTRACT: We establish several new Lyapunovtype inequalities for some nonlinear difference system when the endpoints are not necessarily usual zeros, but rather generalized zeros. Our results generalize in some sense the known ones. As an application, we develop disconjugacy criteria by making use of the obtained inequalities. MSC: 34D20, 39A99. 
Article: Existence of homoclinic orbits for a class of pLaplacian systems in a weighted Sobolev space
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ABSTRACT: By applying the mountain pass theorem and symmetric mountain pass theorem in critical point theory, the existence of at least one or infinitely many homoclinic solutions is obtained for the following pLaplacian system: d d t (  u ˙ ( t )  p − 2 u ˙ ( t ) ) − a ( t )  u ( t )  q − p u ( t ) + ∇ W ( t , u ( t ) ) = 0 , where 1 < p < ( q + 2 ) / 2 , q > 2 , t ∈ R , u ∈ R N , a ∈ C ( R , R ) and W ∈ C 1 ( R × R N , R ) are not periodic in t. MSC: 34C37, 35A15, 37J45, 47J30.  [Show abstract] [Hide abstract]
ABSTRACT: In this work, we establish two new Lyapunovtype inequalities for the 2k2korder difference equation △2kx(n)+(−1)k−1q(n)x(n+1)=0.△2kx(n)+(−1)k−1q(n)x(n+1)=0. Applying our inequalities, we obtain the lower bounds of the eigenvalue for a related eigenvalue problem.  [Show abstract] [Hide abstract]
ABSTRACT: We establish several Lyapunovtype inequalities for quasilinear difference systems, which generalize or improve all related existing ones. Applying these results, we also obtain some lower bounds for the first eigencurve in the generalized spectra.  [Show abstract] [Hide abstract]
ABSTRACT: In this article, we will give several conditions under which the following planar linear discrete Hamiltonian system with perturbations {Delta x(n) = [alpha(n) + alpha(1)(n)]x(n + 1) + [beta(n) + beta(0)(n)] y(n) + f(1)(n, x(n), y(n)), Delta y(n) = [gamma(n) + gamma(0)(n)]x(n + 1)  [alpha(n) + alpha(2)(n)] y(n) + f(2)(n, x(n), y(n)) has the same stability as the corresponding linear system Delta x(n) = alpha(n)x(n + 1) + beta(n)y(n),Delta y(n) = gamma(n)x(n + 1)  alpha(n) y(n). Moreover, these conditions are shown to be necessary and sharp by examples.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, by using elementary analysis, we establish several new Lyapunov type inequalities for the following nonlinear dynamic system on an arbitrary time scale T{xΔ(t)=α(t)x(σ(t))+β(t)y(t)p−2y(t),yΔ(t)=−γ(t)x(σ(t))q−2x(σ(t))−α(t)y(t), when the endpoints are not necessarily usual zeros, but rather, generalized zeros, which generalize and improve all related existing ones including the continuous and discrete cases.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we establish several new Lyapunovtype inequalities for the firstorder nonlinear Hamiltonian system {x′(t)=α(t)x(t)+β(t)y(t)μ−2y(t),y′(t)=−γ(t)x(t)ν−2x(t)−α(t)y(t), which generalize or improve all related existing ones.  [Show abstract] [Hide abstract]
ABSTRACT: We establish several new Lyapunovtype inequalities for some quasilinear dynamic system involving the Laplacian on an arbitrary time scale , which generalize and improve some related existing results including the continuous and discrete cases.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we present some Lyapunov type inequalities for discrete linear scalar Hamiltonian systems when the coefficient c(t) is not necessarily nonnegative valued and when the endpoints are not necessarily usual zeros, but rather, generalized zeros. Applying these inequalities, we obtain some disconjugacy and stability criteria for discrete Hamiltonian systems  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we establish several new Lyapunov type inequalities for linear Hamiltonian systems on an arbitrary time scale T when the endpoints are not necessarily usual zeroes, but rather, generalized zeroes, which generalize and improve all related existing ones including the continuous and discrete cases.  [Show abstract] [Hide abstract]
ABSTRACT: By applying minimax methods in critical point theory, we prove the existence of periodic solutions for the following discrete Hamiltonian systems Δ2u(t1)+∇F(t,u(t))=0, where t∈ℤ, u∈ℝN, F:ℤ×ℝN→ℝ, F(t,x) is continuously differentiable in x for every t∈ℤ and is Tperiodic in t;T is a positive integer.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we establish several new Lyapunovtype inequalities for the nonlinear difference system {Δx(n)=α(n)x(n+1)+β(n)y(n)μ−2y(n),Δy(n)=−γ(n)x(n+1)ν−2x(n+1)−α(n)y(n), when the endpoints are not necessarily usual zeros, but rather, generalized zeros. Our results improve almost all related existing ones.  [Show abstract] [Hide abstract]
ABSTRACT: We establish several sharper Lyapunovtype inequalities for the following evenorder differential equation These results improve some existing ones. 2000 Mathematics Subject Classification: 34B15.  [Show abstract] [Hide abstract]
ABSTRACT: In this article, we establish some stability criteria for the polar linear Hamiltonian dynamic system on time scales by using Floquet theory and Lyapunovtype inequalities. 2000 Mathematics Subject Classification: 39A10.
Publication Stats
111  Citations  
15.86  Total Impact Points  
Top Journals
Institutions

20112013

Hunan University of Technology
Chuchoushih, Hunan, China


20112012

Central South University
 School of Mathematics and Statistics
Ch’angshashih, Hunan, China
