For a class of asymptotically periodic quasilinear Schr？dinger equations with critical growth the existence of ground states is proved.First applying a change of variables the quasilinear Schr？dinger equations are r...For a class of asymptotically periodic quasilinear Schr？dinger equations with critical growth the existence of ground states is proved.First applying a change of variables the quasilinear Schr？dinger equations are reduced to semilinear Schr？dinger equations in which the corresponding functional is well defined in H1 RN .Moreover there is a one-to-one correspondence between ground states of the semilinear Schr？dinger equations and the quasilinear Schr？dinger equations.Then the mountain-pass theorem is used to find nontrivial solutions for the semilinear Schr？dinger equations. Finally under certain monotonicity conditions using the Nehari manifold method and the concentration compactness principle the nontrivial solutions are found to be exactly the same as the ground states of the semilinear Schr？dinger equations.展开更多
In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β（ux^n）x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy prob...In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β（ux^n）x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy problem admits a unique global smooth solution u∈C^∞（（0, T]; H^∞（R）） ∩ C（[0, T]; H^2（R）） ∩ C^1（[0, T]; L^2（R）） under suitable assumptions on the initial data.展开更多
This paper deals with the existence and nonexistence of global positive solutions of the following quasilinear parabolic equations:u t=1m△u m-u n, x∈Ω,t>0 1m·u mv=u p,x∈Ω,t>0 u(x,0)=u 0(x)>0,x∈Ω-w...This paper deals with the existence and nonexistence of global positive solutions of the following quasilinear parabolic equations:u t=1m△u m-u n, x∈Ω,t>0 1m·u mv=u p,x∈Ω,t>0 u(x,0)=u 0(x)>0,x∈Ω-where Ω∈R N is a bounded domain with smooth boundary Ω,m,n,p are positive constants, γ is the outward normal vector. The necessary and sufficient conditions for the global existence of solutions are obtained.展开更多
In this paper we discuss the quasilinear parabolic equation U_■=▽(u^u(1-u)~β.Vu)+■(x,t.u)▽u+C(x,t,u) which is degenerate at u =0 and u=1.Let u(x,t)be a weak solution of the equation satisfying 0<u(x,t)<1.Un...In this paper we discuss the quasilinear parabolic equation U_■=▽(u^u(1-u)~β.Vu)+■(x,t.u)▽u+C(x,t,u) which is degenerate at u =0 and u=1.Let u(x,t)be a weak solution of the equation satisfying 0<u(x,t)<1.Under some assumptions we establish H■lder continuity of u(x,t).展开更多
In this paper the authors consider Cauchy problem of first order quasilinear hyperbolic and prove that existence of its periodic solutions and estimates of life span of solutions. This results reveals the relationship...In this paper the authors consider Cauchy problem of first order quasilinear hyperbolic and prove that existence of its periodic solutions and estimates of life span of solutions. This results reveals the relationship of dissipation and smoothness of periodic solutions.展开更多
In this paper, we discuss the blow-up of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form, and make the accurate estimate of life-span. These results in this paper extend the conclusion...In this paper, we discuss the blow-up of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form, and make the accurate estimate of life-span. These results in this paper extend the conclusion [1-3].展开更多
In this paper,we discuss a class of the quasillinear hyperbolic equations with the inhomogeneous terms: u_■+σ(v)+2α(t)u=0.v_■-u-0 Under the certain of hypothesis.we prove the globally existence theorems of the smo...In this paper,we discuss a class of the quasillinear hyperbolic equations with the inhomogeneous terms: u_■+σ(v)+2α(t)u=0.v_■-u-0 Under the certain of hypothesis.we prove the globally existence theorems of the smooth solutions for its Cauchy problem.展开更多
In this paper, we consider Cauchy problem for a class of quasilinear hyperbolic equations with forced terms, extend and improve the existence in paper[2].
The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form： μt-△φ（μ） = 0 ,where φ ε C1（R^1） is a strictly monotone increasing function. Cle...The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form： μt-△φ（μ） = 0 ,where φ ε C1（R^1） is a strictly monotone increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ＇（.） is permitted to have zero measure. This is an answer to an open problem in [13, p. 288].展开更多
This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of Rp, p>= 1. The me...This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of Rp, p>= 1. The method of penalization is used with a view to obtaining an existence result. However, the former only gives uniform L -estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L . The uniqueness of this EMVS is proved. Classically, it first ensures the existence of a bounded and measurable function U entropy solution and then the strong convergence in Lq of approximate solutions to U.展开更多
We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcrit...We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcritical growth and V（x） is a positive Hlder continuous function which is bounded from below, away from zero, and infΛV（x） 0 such that for all ε∈（0, ε0],the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V（x） as ε→ 0~＋.展开更多
基金The Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXLX_0069)
文摘For a class of asymptotically periodic quasilinear Schr？dinger equations with critical growth the existence of ground states is proved.First applying a change of variables the quasilinear Schr？dinger equations are reduced to semilinear Schr？dinger equations in which the corresponding functional is well defined in H1 RN .Moreover there is a one-to-one correspondence between ground states of the semilinear Schr？dinger equations and the quasilinear Schr？dinger equations.Then the mountain-pass theorem is used to find nontrivial solutions for the semilinear Schr？dinger equations. Finally under certain monotonicity conditions using the Nehari manifold method and the concentration compactness principle the nontrivial solutions are found to be exactly the same as the ground states of the semilinear Schr？dinger equations.
基金Foundation item： Supported by the Sichuan Educational Comittee Science Foundation for Youths（08ZB002） Supported by the National Secience Foundation of Yibin University（2008Z02）
文摘In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
基金Supported by the National Natural Science Foundation of China(10371073)
文摘In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β（ux^n）x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy problem admits a unique global smooth solution u∈C^∞（（0, T]; H^∞（R）） ∩ C（[0, T]; H^2（R）） ∩ C^1（[0, T]; L^2（R）） under suitable assumptions on the initial data.
文摘This paper deals with the existence and nonexistence of global positive solutions of the following quasilinear parabolic equations:u t=1m△u m-u n, x∈Ω,t>0 1m·u mv=u p,x∈Ω,t>0 u(x,0)=u 0(x)>0,x∈Ω-where Ω∈R N is a bounded domain with smooth boundary Ω,m,n,p are positive constants, γ is the outward normal vector. The necessary and sufficient conditions for the global existence of solutions are obtained.
文摘In this paper we discuss the quasilinear parabolic equation U_■=▽(u^u(1-u)~β.Vu)+■(x,t.u)▽u+C(x,t,u) which is degenerate at u =0 and u=1.Let u(x,t)be a weak solution of the equation satisfying 0<u(x,t)<1.Under some assumptions we establish H■lder continuity of u(x,t).
文摘In this paper the authors consider Cauchy problem of first order quasilinear hyperbolic and prove that existence of its periodic solutions and estimates of life span of solutions. This results reveals the relationship of dissipation and smoothness of periodic solutions.
文摘In this paper, we discuss the blow-up of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form, and make the accurate estimate of life-span. These results in this paper extend the conclusion [1-3].
文摘In this paper,we discuss a class of the quasillinear hyperbolic equations with the inhomogeneous terms: u_■+σ(v)+2α(t)u=0.v_■-u-0 Under the certain of hypothesis.we prove the globally existence theorems of the smooth solutions for its Cauchy problem.
文摘In this paper, we consider Cauchy problem for a class of quasilinear hyperbolic equations with forced terms, extend and improve the existence in paper[2].
基金Project supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE(No.[2000]26)the 973 Project of the Ministry of Science and Technology of China(No.2006CB805902)+1 种基金the National Natural Science Foundation of China(No.10571072)the Key Laboratory of Symbolic Computation and Knowledge Engineering of the Ministry of Education of China and the 985 Project of Jilin University.
文摘The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form： μt-△φ（μ） = 0 ,where φ ε C1（R^1） is a strictly monotone increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ＇（.） is permitted to have zero measure. This is an answer to an open problem in [13, p. 288].
文摘This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of Rp, p>= 1. The method of penalization is used with a view to obtaining an existence result. However, the former only gives uniform L -estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L . The uniqueness of this EMVS is proved. Classically, it first ensures the existence of a bounded and measurable function U entropy solution and then the strong convergence in Lq of approximate solutions to U.
基金supported by National Natural Science Foundation of China(Grant Nos.11371160 and 11328101)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.#IRT13066)
文摘We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcritical growth and V（x） is a positive Hlder continuous function which is bounded from below, away from zero, and infΛV（x） 0 such that for all ε∈（0, ε0],the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V（x） as ε→ 0~＋.
