Publications (14)8.77 Total impact
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ABSTRACT: In this paper, we consider the existence of a nontrivial weak solution to a quasilinear elliptic equation with singular weights and multiple critical exponents in the whole space. Firstly, we get the existence of a local Palais–Smale sequence by verifying the geometric conditions of the Mountain Pass Lemma. Secondly, we study the concentration properties of the Palais–Smale sequence of a zero weak limit. Thirdly, we deduce by contradiction to eliminate the possibility of a zero weak limit case. Lastly, applying a monotonic inequality, we shall prove that the nontrivial weak limit of the Palais–Smale sequence is indeed a weak solution.Nonlinear Analysis 05/2010; 72(91072):36493658. DOI:10.1016/j.na.2009.12.046 · 1.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we study the asymptotic behavior of radial extremal functions to an inequality involving Hardy potential and critical Sobolev exponent. Based on the asymptotic behavior at the origin and the infinity, we shall deduce a strict inequality between two best constants. Finally, as an application of this strict inequality, we consider the existence of a nontrivial solution of a quasilinear Brezis–Nirenberg type problem with Hardy potential and critical Sobolev exponent.Nonlinear Analysis 08/2009; 71(3471):845859. DOI:10.1016/j.na.2008.10.114 · 1.33 Impact Factor 
Article: Existence results for Brezis–Nirenberg problems with Hardy potential and singular coefficients
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ABSTRACT: In this paper, we consider the existence of nontrivial solutions to semilinear Brezis–Nirenberg type problems with Hardy potential and singular coefficients. First, we shall study the corresponding eigenvalue problem, and obtain some basic properties of eigenvalues and asymptotic estimates of the eigenfunctions and approximating eigenfunctions. Secondly, we consider the extremal functions of the best embedding constant, and get some crucial estimates for the cutoff function of the extremal functions. Thirdly, applying different variational theorems for distinct cases of those parameters appearing in the equation, we obtain two existence results for nontrivial solutions to semilinear Brezis–Nirenberg type problems. Our existence results are divided into nonresonant and resonant cases.Nonlinear Analysis 10/2007; 67(767):20912106. DOI:10.1016/j.na.2006.09.018 · 1.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we study the asymptotic behavior of radial extremal functions to an inequality involving Hardy potential and critical Sobolev exponent. Based on the asymptotic behavior at the origin and the infinity, we shall deduce a strict inequality between two best constants. Finally, as an application of this strict inequality, we consider the existence of nontrivial solution of a quasilinear BrezisNirenberg type problem with Hardy potential and critical Sobolev exponent.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we consider the existence and nonexistence of nontrivial solutions to quasilinear Brezis–Nirenbergtype problems with singular weights. First, we shall obtain a compact imbedding theorem which is an extension of the classical Rellich–Kondrachov compact imbedding theorem, and consider the corresponding eigenvalue problem. Secondly, we deduce a Pohozaevtype identity and obtain a nonexistence result. Thirdly, thanks to the generalized concentration compactness principle, we will give some abstract conditions when the functional satisfies the (PS)c condition. Finally, basing on the explicit form of the extremal function, we will obtain some existence results.Nonlinear Analysis 08/2005; 62(462):703725. DOI:10.1016/j.na.2005.03.095 · 1.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, using Mountain Pass Lemma and Linking Argument, we prove the existence of nontrivial weak solutions for the Dirichlet problem for the superlinear equation of CaffarelliKohnNirenberg type in the case where the parameter $\lambda\in (0, \lambda_2)$, $\lambda_2$ is the second positive eigenvalue of the quasilinear elliptic equation of CaffarelliKohnNirenberg type.05/2004; 
Article: Multiple solutions to a CaffarelliKohnNirenberg type equation with asymptotically linear term
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ABSTRACT: We study the existence of multiple solutions to a CaffarelliKohnNirenberg type equation with asymptotically linear term at infinity div(x αp Du p2 Du)=x (α+1)p+c f(u)inΩ,u=0on∂Ω, where Ω⊂ℝ n is a bounded regular domain such that 0∈Ω, 1<p<n, 0≤α<np p, c>0, and f∈C(ℝ) is such that f(t)=f(t) for all t∈ℝ and satisfies: (f1) lim t→0 f(t) t p2 t=0, (f2) lim t→+∞ f(t) t p2 t=l<+∞. In this case, the wellknown AmbrosettiRabinowitz type condition doesn’t hold, hence it is difficult to verify the classical (PS) c condition. To overcome this difficulty, we use an equivalent version of Cerami’s condition, which allows the more general existence result.05/2004; 
Article: The solvability of BrezisNirenberg type problems of singular quasilinear elliptic equation
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ABSTRACT: In this paper, we consider the existence and nonexistence of nontrivial solution to a BrezisNirenberg type problem with singular weights. First, we obtain a compact imbedding theorem which is an extension of the classical RellichKondrachov compact imbedding theorem, and consider the corresponding eigenvalue problem. Secondly, we deduce a Pohozaev type identity and obtained a nonexistence result. Thirdly, based on a generalized concentration compactness principle, we will give some abstract conditions when the functional satisfies the (PS)$_c$ condition. Finally, based on the explicit form of the extremal function, we will obtain some existence results to the problem.  [Show abstract] [Hide abstract]
ABSTRACT: In this article, using the Mountain Pass Lemma due to Ambrosetti and Rabinowitz, we obtain the existence of nontrivial stationary solutions of Generalized Kadomtsev–Petviashvili (GKP) equation in a bounded domain with smooth boundary and for superlinear nonlinear term f (u) which satisfies some growth condition. Based on a Pohozaev type variational identity for cylindrical symmetric solution, we obtain the nonexistence of the nontrivial cylindrical symmetric solution for supercritical nonlinearity, i.e. f(u)=u p −2 u where .Applicable Analysis 11/2003; 82(11):10391048. DOI:10.1080/00036810310001613124 · 0.80 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we shall investigate the existence of multiple (positive) weak solutions for the Dirichlet problem of the pLaplacian with singularity and cylindrical symmetry. The results depends heavily on parameters n,p,q,r,s and λ>0. By the technical decomposition of the associated Nehari manifold into three parts Λ+,Λ− and Λ0, and some compactness condition such as (PS) condition or local (PS) condition ((PS)c condition) at certain level of energy, we obtain two nonnegative minimizers of the energy functional on Λ+ and Λ−, respectively.Nonlinear Analysis 11/2003; 55(3):217232. DOI:10.1016/S0362546X(03)002244 · 1.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, using Mountain Pass Lemma and Linking Argument, we prove the existence of nontrivial weak solutions for the Dirichlet problem of the superlinear pLaplacian equation – Δ p =:div(∇u p2 ∇u)=λV(x)u p2 u+f(x,u)inΩ,u=0on∂Ω,(P) where p>1, Ω is a bounded domain of ℝ N , V(x) is a changing sign function belonging to L s , for some s>N p, if 1<p<N, and s=1 if p>N and λ is a real parameter – in the case where the eigenvalue parameter λ∈(0,λ 2 ), λ 2 is the second positive eigenvalue of the pLaplacian with indefinite weights.Nonlinear Analysis 08/2003; 54(554):949958. DOI:10.1016/S0362546X(03)001202 · 1.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, using the Mountain Pass Lemma without (PS) condition due to Ambrosetti and Rabinowitz, we obtain the existence of the nontrivial solitary waves of Generalized KadomtsevPetviashvili equation in multidimensional spaces and for superlinear nonlinear term f (u) which satisfies some growth condition. By the Pohozaev type variational identity, we obtain the nonexistence of the nontrivial solitary waves for power function nonlinear case, i.e. f (u) = up where p 2(2n  1)/(2n  3).01/2003;  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we study the existence of multiple solutions to a CaffarelliKohnNirenberg type equation with asymptotically linear term at infinity. In this case, the wellknown AmbrosettiRabinowtz type condition doesn't hold, hence it is difficult to verify the classical (PS)$_c$ condition. To overcome this difficulty, we use an equivalent version of Cerami's condition, which allows the more general existence result.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we study the existence of multiple stationary solutions of Generalized KadomtsevPetviashvili (Abbr. GKP) equation in a bounded domain with smooth boundary and for superlinear nonlinear term f(u) = ‚jujp¡2u + jujq¡2u where 1 • p;q < 2⁄ = 2(2n¡1) 2n¡3 . Our methods are based on variational methods, and the results are divided into two cases according to the dierent values of the parameters p; q.01/2002;
Publication Stats
129  Citations  
8.77  Total Impact Points  
Top Journals
Institutions

20052010

University of Science and Technology of China
Luchow, Anhui Sheng, China


2003

National University of Colombia
Μπογκοτά, Bogota D.C., Colombia
