2m阶Dirichlet边值问题的多解(英文)

本文讨论了非线性2m阶Dirichlet边值问题多解的存在性.在非线性项满足一定条件时,通过有效地利用锥中的不动点指数理论和解的反对称延拓法,得到关于变号解的一些新的存在结果.确切地说,得到该2m阶边值问题至少存在两个正解,两个负解和多个变号解.     

跳跃非线性条件下椭圆边值问题的变号解和多解存在性

本文应用Banach空间常微分方程和极大极小理论,特别是相对山路引理研究了零点和无穷远点跳跃非线性条件下椭圆边值问题的变号解和多解,得到新的变号解和多解存在性定理,最后我们得到6个非平凡解的存在性.     

跳跃非线性条件下椭圆边值问题的变号解和多解存在性

本文应用Ｂａｎａｃｈ空间常微分方程和极大极小理论,特别是相对山路引理研究了零点和无穷远点跳跃非线性条件下椭圆边值问题的变号解和多解,得到新的变号解和多解存在性定理,最后我们得到６个非平凡解的存在性．     

一致椭圆型算子边值问题变号解的存在性

利用Banach空间锥理论、算子的指数理论、上下解理论研究了含有一致椭圆型算子的椭圆边值问题变号解的存在性,同时分别得到了一个正解和一个负解.特别当非线性项是奇函数时,该边值问题至少存在一个正解,一个负解和两个变号解.     

一类具衰减位势的Schrdinger-Poisson方程变号基态解的存在性

本文研究一类具有衰减位势的Schrdinger-Poisson方程变号基态解的存在性,应用Nehari流形和变分方法,我们得到了该类方程存在一个变号基态解.进一步,如果该问题具有对称性时,我们证明了无穷多个非平凡解的存在性.在本文的结论中非线性项只要求是连续的.     

一个带限制的椭圆特征问题的多解和变号解

利用变分方法证明了一个带限制的半线性椭圆特征问题变号解的存在性.所获得的3个解,1个是正解、1个是负解、1个是变号解.在某些附加条件下证明了多重变号解的存在性.     

一类四阶非线性椭圆问题变号解的存在性

通过建立一个新空间,在新空间中讨论了一个含Hardy位势的四阶非线性椭圆问题变号解的存在性.在一个环绕定理下,得到了问题变号解的存在性.     

一类带有变号二阶四点奇异边值问题的正解

本文研究了一类带有变号二阶四点奇异边值问题的正解的存在性.首先我们给出其格林函数,其次我们结合下解的方法和拓扑度理论得到了其正解的存在性.最后给出-个例题阐述得到结果的正确性.本文的结果是新的,并且扩展了已有的结果.     

带Hardy位势的双调和椭圆方程的正负解及变号解

本文讨论带Hardy位势的四阶渐近线性椭圆方程,应用变分方法,我们得到了正负解及变号解的存在性.     

二阶非线性差分方程边值问题的多解性与变号解

利用下降流不变集方法并结合变分技巧,本文得到二阶非线性差分方程在Robin边界条件下存在正解、负解以及变号解的充分条件的结果.最后运用相关例子验证定理的可行性.     

Sign-changing solutions for some fourth-order nonlinear elliptic problems

In this paper, we consider the existence and multiplicity of sign-changing solutions for some fourth-order nonlinear elliptic problems and some existence and multiple are obtained. The weak solutions are sought by means of sign-changing critical theorems.     

Existence and location results for sign-changing solutions for three-point boundary value problems using Leray-Schauder degree

In this paper, by using the modification function technique and the Leray-Schauder degree method some existence and multiplicity results for sign- changing solutions of certain three-point boundary value problems are obtained. The main result of this paper is an improvement on a former existence result for sign-changing solutions of certain three-point boundary value problems.     

Existence and location results for sign-changing solutions for three-point boundary value problems using Leray-Schauder degree

In this paper, by using the modification function technique and the Leray-Schauder degree method some existence and multiplicity results for sign- changing solutions of certain three-point boundary value problems are obtained. The main result of this paper is an improvement on a former existence result for sign-changing solutions of certain three-point boundary value problems.     

Solvability for a higher-order Hadamard fractional differential model with a sign-changing nonlinearity dependent on the parameter $\varrho$

Until now most of the results are obtained in the sense of fractional derivatives such as Caputo and Riemann-Liouville, and there are few models using the Hadamard fractional derivatives. In this paper, based on the properties of the Green"s function, the existence of positive solutions are obtained for a Hadamard fractional differential equation with a higher-order sign-changing nonlinearity under some conditions by the fixed point theorem, and the existence of positive solutions is dependent on the parameter $\varrho$ for the Semipositive problem.     

On sign-changing solutions for nonlinear operator equations

In this paper, the existence of sign-changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory. The main theorems are some new three-solution theorems which are different from the famous Amann's and Leggett-Williams' three-solution theorems as well as the results in [F. Li, G. Han, Generalization for Amann's and Leggett-Williams' three-solution theorems and applications, J. Math. Anal. Appl. 298 (2004) 638-654]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution. Furthermore, the theoretical results are successfully applied to both integral and differential equations.     

非线性算子方程的变号解及其应用

利用锥理论讨论了非线性算子方程变号解的存在性,所得结果在理论上推广了相关文献的结论. 作为应用,考虑了二阶三点边值问题, 得到了新的结论.     

具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题的非平凡解

应用拓扑度方法证明了具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题非平凡解的存在性,其中非线性项f可以不是非负的但下方有界.给出了正解存在性的两个推论,它们是非线性项f非负情形已有结论的推广.通过两个例子来说明主要结论,例子的混合边值条件包含变号系数的多点条件和变号核的积分条件.     

On elliptic problems involving critical Hardy-Sobolev exponents and sign-changing function

In this paper, we deal with the existence and nonexistence of nonnegative nontrivial weak solutions for a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and a sign-changing function. Some existence results are obtained by splitting the Nehari manifold and by exploring some properties of the best Hardy-Sobolev constant together with an approach developed by Brezis and Nirenberg.     

Sign-changing solutions of nonlinear elliptic equations

In this survey article, we recall some known results on existence and multiplicity of sign-changing solutions of elliptic equations. Methods for obtaining sign-changing solutions developed in the last two decades will also be briefly revisited.