In this paper, we consider a class of N-Laplacian equations involving critical growth{-?_N u = λ|u|^(N-2) u + f(x, u), x ∈ ?,u ∈ W_0^(1,N)(?), u(x) ≥ 0, x ∈ ?,where ? is a bounded domain with smooth boundary in R...In this paper, we consider a class of N-Laplacian equations involving critical growth{-?_N u = λ|u|^(N-2) u + f(x, u), x ∈ ?,u ∈ W_0^(1,N)(?), u(x) ≥ 0, x ∈ ?,where ? is a bounded domain with smooth boundary in R^N(N > 2), f(x, u) is of critical growth. Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti, we prove the existence of a nontrivial solution for any λ > λ_1, λ = λ_?(? = 2, 3, · · ·), and λ_? is the eigenvalues of the operator(-?_N, W_0^(1,N)(?)),which is defined by the Z_2-cohomological index.展开更多
To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems...To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems with n Laplacian operators are established in three singular cases.展开更多
We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential crit...We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential critical growth.The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.展开更多
We study exponential decay property of radial ground states to a class of N-Laplacian elliptic equations in the whole space R^N. Their decay rates as /x/→∞ are obtained explicitly.
基金Supported by Shanghai Natural Science Foundation(15ZR1429500)NNSF of China(11471215)
文摘In this paper, we consider a class of N-Laplacian equations involving critical growth{-?_N u = λ|u|^(N-2) u + f(x, u), x ∈ ?,u ∈ W_0^(1,N)(?), u(x) ≥ 0, x ∈ ?,where ? is a bounded domain with smooth boundary in R^N(N > 2), f(x, u) is of critical growth. Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti, we prove the existence of a nontrivial solution for any λ > λ_1, λ = λ_?(? = 2, 3, · · ·), and λ_? is the eigenvalues of the operator(-?_N, W_0^(1,N)(?)),which is defined by the Z_2-cohomological index.
文摘To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems with n Laplacian operators are established in three singular cases.
基金Natural Science Foundation of China(Grant Nos.11601190 and 11661006)Natural Science Foundation of Jiangsu Province(Grant No.BK20160483)Jiangsu University Foundation Grant(Grant No.16JDG043)。
文摘We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential critical growth.The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.
文摘We study exponential decay property of radial ground states to a class of N-Laplacian elliptic equations in the whole space R^N. Their decay rates as /x/→∞ are obtained explicitly.
