具ρ-aplacian算子非齐次辊舍型二阶微分方程多点边值问题(英文)

A class of multi-point boundary value problems are studied.Easily verified suffcient conditions to guarantee the existence of at least one solutions of above mentioned BVPs are established.The examples are presented to illustrate the main results.     

含有p-Laplacian算子的非齐次多点边值问题

研究非齐次边界条件下,含有p-Laplacian算子的微分方程的可解性.应用Banach空间中的Krasnoselskii不动点定理,得到了边值问题正解的存在性结果.     

一维p-Laplacian方程正解的存在性

本文考虑一维p-Laplacian非线性边值问题(ψ(u′))′+f(t,u)=0,αψ(u(0))—βψ(u′(0))=O,γψ(u(1))+δψ(u′(1))=0,其中ψ(s):=|s|~(p-2)s,P>1.通过应用Krasnoselskii锥不动点定理,建立了该问题存在多个正解的充分条件,推广并丰富了以往文献的一些结论.     

具p-Laplace算子型泛函差分方程的正解

In this paper,the author studies the boundary value problems for a p-Laplacian functional difference equation.By using a fixed point theorem in cones,sufficient conditions are established for the existence of the positive solutions.     

测度链上p-Laplacian边值问题的三个正对称解

该文研究了p-Laplacian动力边值问题（g（u^△（t）））△＋a（t）f（t，u（t））=0，t∈[0，T]T,u（0）=u（T）=w，u△（0）=-u^△（T）正解的存在性．其中W是非负实数，g（v）=｜v｜p-2v1 P＞1．根据对称技巧和五泛函不动点定理，证明了边值问题至少有三个正的对称解，同时，给出了一个例子验证了我们的结果。     

测度链上p-Laplacian 边值问题的三个正对称解

该文研究了p-Laplacian 动力边值问题 (g(u^△(t)))^▽+a(t)f(t, u(t))=0, t ∈ [0, T] _T, u(0)=u(T)=w, u^△(0)=-u^△(T) 正解的存在性. 其中w是非负实数, g(ν)=|ν| ^p-2ν, p>1 . 根据对称技巧和五泛函不动点定理, 证明了边值问题至少有三个正的对称解, 同时, 给出了一个例子验证了我们的结果.     

某些一阶非齐次中立型微分差分方程的振动性

该文讨论了 d/dt[x(t) cx(t-τ)] P(t)x(t-σ) f(t)=0,t≥t_0一阶非齐次中立型微分差分方程的振动性.得到了一些方程振动的充分条件,推广了某些齐次方程的振动结果.     

二阶P—Laplacian问题三个正解的存在性

本文要讨论了二阶P—Laplaci!an方程边值问题{△（φ（Au（t-1）））＋a（t），（t，u（t））=0，t∈N[1，T＋1]；△u（O）=0，u（T＋2）=0三个正解的存在性。通过利用一个三解不动点定理，证明了当，（t，x）在满足较弱条件时该方程至少三个正解的存在性。     

三阶p-Laplacian非齐次边值问题多重正解的存在性

本文应用凸锥上的一个不动点定理,讨论了一类含p-Laplacian算子的三阶非齐次边值问题多重正解的存在性,得到了这类边值问题至少存在三个正解的充分条件,并给出了一个实例.     

Existence of positive solutions for higher-order generalized p-Laplacian BVPs

In this paper, we provide suitable conditions on the function f(t, u₁, …, u_n−1) such that the higher-order generalized p-Laplacian boundary value problem

has at least one positive solution.Moreover, we shall apply this result to establish several existence theorems which guarantee the multiple positive solutions.     

一类共振条件下的高阶p-Laplacian算子多点边值问题

主要讨论了下列n阶带p-Laplacian算子多点边值问题在共振条件下解的存在性.(Φp(x(n-1)))′+f(t,x,x′,…,x(n-2))=0,0相似文献   

Minimization of Eigenvalues of One-Dimensional p-Laplacian with Integrable Potentials

In this paper, we will use the variational method and limiting approach to solve the minimization problems of the Dirichlet/Neumann eigenvalues of the one-dimensional p-Laplacian when the L ¹ norm of integrable potentials is given. Combining with the results for the corresponding maximization problems, we have obtained the explicit results for these eigenvalues.     

Three positive solutions for delay differential equation BVPs with p-Laplacian on infinite interval

In this paper we investigate the existence of three positive solutions for delay differential equation boundary value problem with p-Laplacian on infinite interval. By using the fixed point theorem in a cone introduced by Avery and Petereson, the existence of at least three positive solutions is obtained under suitable growth conditions imposed on the nonlinear term. As an application, one example is given to demonstrate our main result. To some extend, our paper complements and generalize the known results.     

四阶超线性奇异P—Laplacian边值问题的正解

该文利用锥上的不动点定理,给出四阶超线性奇异p-Laplacian边值问题正解存在的充分必要条件.所给出的条件与非线性项的可积性有关.     

Spectrum of One-Dimensional p-Laplacian with an Indefinite Integrable Weight

Motivated by extremal problems of weighted Dirichlet or Neumann eigenvalues, we will establish two fundamental results on the dependence of weighted eigenvalues of the one-dimensional p-Laplacian on indefinite integrable weights. One is the continuous differentiability of eigenvalues in weights in the Lebesgue spaces L ^γ with the usual norms. Another is the continuity of eigenvalues in weights with respect to the weak topologies in L ^γ spaces. Here 1 ≤ γ ≤ ∞. In doing so, we will give a simpler explanation to the corresponding spectrum problems, with the help of several typical techniques in nonlinear analysis such as the Fréchet derivative and weak* convergence.     

含有一阶导数的一维p-Laplace方程的正解

通过利用积分方程全连续算子的不动点指数对含有一阶导数的一维p-L ap lace方程建立了一个存在定理.这个定理表明此p-L ap lace方程必有一个正解,只要非线性项在某个有界集合上的“最大高度”是适当的.     

p-Laplacian算子方程在射线上多点边值问题三个正解的存在性

利用Avery-Peterson不动点定理,在射线上讨论了如下p-Laplacian算子方程多点边值问题,{(φp(u′))′(t)+q(t)f(t,u(t),u′(t))=0,0相似文献   

一维p-Laplacian方程奇异边值问题的正解

本文讨论了一维p-Laplacian方程奇异边值问题的正解的存在性,其中函数f(t,x)可能在t=0,1都有奇点