arXiv subjects

Benjin Xuan

Publications and source records attributed to Benjin Xuan.

4 recordsLinked to original sources

arXiv2007

Asymptotic behavior of extremal functions to an inequality involving Hardy potential and critical Sobolev exponent

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 Brezis-Nirenberg type problem with Hardy potential and critical Sobolev exponent.

math.AP↗

arXiv2004

Existence results for a superlinear singular equation of Caffarelli-Kohn-Nirenberg type

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 Caffarelli-Kohn-Nirenberg type in the case where the parameter $λ\in (0, λ_2)$, $λ_2$ is the second positive eigenvalue of the quasilinear elliptic equation of Caffarelli-Kohn-Nirenberg type.

math.AP↗

arXiv2004

Multiple solutions to a Caffarelli-Kohn-Nirenberg type equation with asymptotically linear term

In this paper, we study the existence of multiple solutions to a Caffarelli-Kohn-Nirenberg type equation with asymptotically linear term at infinity. In this case, the well-known Ambrosetti-Rabinowtz 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.

math.AP↗

arXiv2004

The solvability of Brezis-Nirenberg type problems of singular quasilinear elliptic equation

In this paper, we consider the existence and non-existence of non-trivial solution to a Brezis-Nirenberg type problem with singular weights. First, we 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 Pohozaev type identity and obtained a non-existence 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.

math.AP↗