Here we generalize the "BBH"-asymptotic analysis to a simplified mathematical model for tho planar ferromaguets and antiferromagnets. To develop such a static theory is a necessary step for a rigorous mathem...Here we generalize the "BBH"-asymptotic analysis to a simplified mathematical model for tho planar ferromaguets and antiferromagnets. To develop such a static theory is a necessary step for a rigorous mathematical justification of dynamical laws for the magnetic vortices formally derived in [1] and [2].展开更多
1 Introduction We want to investigate the following boundary value problem:where m】1, n】1, p≥1 and m】p. As for a, the following properties will be assumed: (A.1) a(r)∈C^1 ([0, ∞)) and a(r)】0 for any r∈(0, ∞);...1 Introduction We want to investigate the following boundary value problem:where m】1, n】1, p≥1 and m】p. As for a, the following properties will be assumed: (A.1) a(r)∈C^1 ([0, ∞)) and a(r)】0 for any r∈(0, ∞); (A.2) there exists α】0 such that (r-α)a(r)≥0 for any r∈[0, ∞). The initial value problem corresponding to (1.1) is the following Cauchy problem:展开更多
This note deals with the blow up set for a non-cooperative noallnear parabolic differential system and generalizes the theorem 3. 2 and 3. 5 of reference [1]. That is, it is proved that the blow up set consists of a s...This note deals with the blow up set for a non-cooperative noallnear parabolic differential system and generalizes the theorem 3. 2 and 3. 5 of reference [1]. That is, it is proved that the blow up set consists of a single point x=0 without the restriction p】q.展开更多
Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved...Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved that there is no non-radial positive solution.展开更多
In this paper, the nonexistence of positive entire solutions for div(|Du| p-2 Du)q(x)f(u),x∈R N, is established, where p】1,Du=(D 1u,...,D Nu),q∶R N→(0,∞) and f∶(0,∞)→(0,∞) are continuous fun...In this paper, the nonexistence of positive entire solutions for div(|Du| p-2 Du)q(x)f(u),x∈R N, is established, where p】1,Du=(D 1u,...,D Nu),q∶R N→(0,∞) and f∶(0,∞)→(0,∞) are continuous functions.展开更多
In this paper, we establish the existence of positive radially symmetric solutions of div(|Du|p-2Du) + λf(r,u(r) ) = 0 in domain R1 < r < R0 or 0 < r < ∞ with a variety of Dirichlet boundary conditions. ...In this paper, we establish the existence of positive radially symmetric solutions of div(|Du|p-2Du) + λf(r,u(r) ) = 0 in domain R1 < r < R0 or 0 < r < ∞ with a variety of Dirichlet boundary conditions. The function f is allowed to be singular when u = 0.展开更多
Existence and multiplicity results of positive radially symmetric solution ofthe eigenvalue problemsare obtained for fi being a N-ball or an annulus via Leray-Schauder degreetheory and variational method.
基金Supported by the Dean's Dissertation FellowshipSupported by a NSF grant
文摘Here we generalize the "BBH"-asymptotic analysis to a simplified mathematical model for tho planar ferromaguets and antiferromagnets. To develop such a static theory is a necessary step for a rigorous mathematical justification of dynamical laws for the magnetic vortices formally derived in [1] and [2].
基金Project supported by the National Natural Science Foundation of China.
文摘1 Introduction We want to investigate the following boundary value problem:where m】1, n】1, p≥1 and m】p. As for a, the following properties will be assumed: (A.1) a(r)∈C^1 ([0, ∞)) and a(r)】0 for any r∈(0, ∞); (A.2) there exists α】0 such that (r-α)a(r)≥0 for any r∈[0, ∞). The initial value problem corresponding to (1.1) is the following Cauchy problem:
文摘This note deals with the blow up set for a non-cooperative noallnear parabolic differential system and generalizes the theorem 3. 2 and 3. 5 of reference [1]. That is, it is proved that the blow up set consists of a single point x=0 without the restriction p】q.
基金Supported by the Youth Foundations of National Education Commuttee the Committee on Science and Technology of Henan Province
文摘Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved that there is no non-radial positive solution.
文摘In this paper, the nonexistence of positive entire solutions for div(|Du| p-2 Du)q(x)f(u),x∈R N, is established, where p】1,Du=(D 1u,...,D Nu),q∶R N→(0,∞) and f∶(0,∞)→(0,∞) are continuous functions.
文摘In this paper, we establish the existence of positive radially symmetric solutions of div(|Du|p-2Du) + λf(r,u(r) ) = 0 in domain R1 < r < R0 or 0 < r < ∞ with a variety of Dirichlet boundary conditions. The function f is allowed to be singular when u = 0.
文摘Existence and multiplicity results of positive radially symmetric solution ofthe eigenvalue problemsare obtained for fi being a N-ball or an annulus via Leray-Schauder degreetheory and variational method.
