带有Neumann边界的方程组多个正解存在性

研究带有Neumann边界条件的拟线性方程组的正解问题.在不同参数条件下,主要利用特征值理论和Nehari流形给出了方程组正解的存在性和多解性.这一结论很好的推广了已有的结果.     

Existence of positive solutions for a general nonlinear eigenvalue problem

Let Ω R n be a bounded domain, H = L 2 (Ω), L : D(L) H → H be an unbounded linear operator, f ∈ C(■× R, R) and λ∈ R. The paper is concerned with the existence of positive solutions for the following nonlinear eigenvalue problem Lu = λf (x, u), u ∈ D(L), which is the general form of nonlinear eigenvalue problems for differential equations. We obtain the global structure of positive solutions, then we apply the results to some nonlinear eigenvalue problems for a second-order ordinary differential equation and a fourth-order beam equation, respectively. The discussion is based on the fixed point index theory in cones.     

非线性特征值问题正解的存在性

证明了四阶边值问题y(4) =λα( x) f ( y( x) ) ,　 0 0且充分小时正解的存在性 .其中 ,α:[0 ,1 ]→ R连续 ,f ( 0 ) >0 .本文的工具是L eray- Schauder不动点定理 [4] .     

A theorem on S-shaped bifurcation curve for a positone problem with convex-concave nonlinearity and its applications to the perturbed Gelfand problem

We study the bifurcation curve and exact multiplicity of positive solutions of the positone problem

     

Existence and bifurcation of positive solutions of a semilinear elliptic problem on {\Bbb R}^N

Existence of positive solutions of a semilinear elliptic problem on , arising from population genetics is obtained. We use an approximation procedure, by accumulation of branches of solutions of the problem stated on balls of sufficiently large radia. Received January 19, 1996     

On the exactness of an S-shaped bifurcation curve

For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for .

     

一类四阶两点边值问题正解的存在性

运用上下解方法及拓扑度理论讨论了非齐次边界条件下四阶两点边值问题u″″(t)=f(u(t)),t∈(0,1),u(0)=u″(0)=u″(1)=0,u(1)=λ,其中λ＞0为参数,f∈C([0,+∞),[0,+∞)).在非线性项满足一定的增长条件下,获得了上述问题存在正解时λ的取值范围.     

二阶三点边值问题正解的存在性

利用不动点指数定理研究了一类二阶非线性常微分方程的三点边值问题正解的存在性问题,得到了至少存在一个或无穷多个正解的几个充分条件.     

一类渐近线性Neumann问题正解的存在性

利用变分法获得了一类渐近线性N eum ann问题正解的存在性结果.     

Existence of multiple positive solutions for inhomogeneous Neumann problem

In this paper, we study the existence and nonexistence of multiple positive solutions for the inhomogeneous Neumann boundary value problem

(∗)     

Existence and bifurcation of positive solutions for fractional p$$ p $$-Kirchhoff problems

In this paper, we are interested in the existence and bifurcation of positive solutions for Kirchhoff-type eigenvalue problems involving the fractional $p$-Laplacian. First, we investigate the properties of the first eigenvalue for fractional $p$-Laplacian equations with weighted functions. Furthermore, by using fixed-point argument and modified global bifurcation theorem of Rabinowitz, together with topological degree theory, we obtain the existence of unbounded continuum of positive weak solutions to Kirchhoff-type equations with subcritical and critical nonlinearities, where the bifurcation emanates from $(\mathrm{0,0})$. It is worth mentioning that our main results fill in some gaps of the available results.     

一类带导数项的非线性特征值问题正解的存在性

应用 Schauder不动点定理 ,证明了带导数项的非线性特征值问题 :　　 u″+λa( t) f ( u,u′) =0 ,0 0充分小 ,f :[0 ,∞ )× R→ R连续且 f( 0 ,0 ) >0 .     

一类奇异边值问题正解的存在性

借助上下解方法和锥拉伸与锥压缩不动点定理研究了二阶非线性奇异边值问题u″ λf(t,u(t))=0,0相似文献   

Existence of symmetric positive solutions for a boundary value problem with integral boundary conditions

This paper studies the existence of symmetric positive solutions for a second-order nonlinear ordinary differential equation with integral boundary conditions by applying the theory of fixed point index in cones. For the demonstration of the results, an illustrative example is presented.     

Existence of positive solutions for second-order boundary value problem with one parameter

In the case of not requiring f(t,u) to be nonnegative, by transforming the boundary value problem into the integral equation system, and applying the fixed point index theory, the author studies the following second-order boundary value problem with one parameter