In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
In this paper,we consider the following systems x″+ Bx′+ gradG(x,t) = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are c...In this paper,we consider the following systems x″+ Bx′+ gradG(x,t) = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are consequences of Theorem 2 in this paper if‖B‖2<1.展开更多
This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k ...This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].展开更多
In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj (α^ij (x, t, u)Diψ(u)) +b^i (t, u)Diu+C(x, t, u) = 0, and obtain the existence, un...In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj (α^ij (x, t, u)Diψ(u)) +b^i (t, u)Diu+C(x, t, u) = 0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.展开更多
The paper studies a class of nonlinear elliptic partial differential equations on a compact Riemannian manifold (M,g) with some curvature restriction. The authors try to prove some uniqueness and nonexistent results...The paper studies a class of nonlinear elliptic partial differential equations on a compact Riemannian manifold (M,g) with some curvature restriction. The authors try to prove some uniqueness and nonexistent results for the positive solutions of the equations concerned.展开更多
The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in s...The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in some cases asymptotic behaviour.展开更多
文摘In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
文摘In this paper,we consider the following systems x″+ Bx′+ gradG(x,t) = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are consequences of Theorem 2 in this paper if‖B‖2<1.
文摘This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].
基金Foundation item: Supported by National Science Foundation of China(10572156) Supported by Natural Science Foundation of Henan Province(0211010900) Supported by National Science Foundation of Department of Education of Henan Province(200510465001)
文摘In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj (α^ij (x, t, u)Diψ(u)) +b^i (t, u)Diu+C(x, t, u) = 0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.
文摘The paper studies a class of nonlinear elliptic partial differential equations on a compact Riemannian manifold (M,g) with some curvature restriction. The authors try to prove some uniqueness and nonexistent results for the positive solutions of the equations concerned.
基金Project supported by the Swiss National Science Foundation under the contract#20-67618.02.
文摘The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in some cases asymptotic behaviour.