共查询到20条相似文献,搜索用时 93 毫秒
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考察了一类具p-Laplacian算子三阶m点边值问题的三个正解.首先利用二阶m点边值问题的Green函数把该类问题转化为一个等价的积分方程,在适当的锥上应用Avery-Peteron不动点定理讨论该类积分方程的正解存在性,从而得到了正解存在的充分条件. 相似文献
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非线性一维p-Laplace方程的两正解存在定理 总被引:2,自引:1,他引:1
姚庆六 《应用泛函分析学报》2005,7(1):28-38
考察了一类非线性一维p-Laplace方程正解的多解性.主要结论表明,即使非线性项在0点和无穷远处不满足通常的增长条件,该方程仍可能有两个正解. 相似文献
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《数学的实践与认识》2019,(22)
利用锥拉伸与锥压缩不动点定理,研究了一类带参数和时滞的Laplacian型方程边值问题的正解,得到了多个正解存在的充分条件.所得结论拓展了时滞方程的研究领域,为时滞方程的研究带来了动力与活力. 相似文献
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本文研究Riemann流形上的改进的p-Laplace方程,运用截断函数的估计、Hessian比较定理和Laplace比较定理,得到该方程正解的梯度估计.并应用该结论,得到在Riemann流形上关于改进的p-Laplace方程正解的Harnack不等式和Liouville型定理. 相似文献
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研究二阶带时标的非线性奇异动力方程m点边值问题的正解,利用锥上的混合单调不动点定理,得到了正解的存在性和唯一性.本文中方程的非线性项可能是奇异的.并举例说明相应的结果. 相似文献
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研究了一类三阶非线性变系数非自治中立型变时滞差分方程正解的存在性,给出了该类方程存在最终正解的几个充分条件,推广了已有文献的某些结果. 相似文献
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一类四队两点边值问题正解的存在性 总被引:11,自引:0,他引:11
在边值条件y(0)=y(1)=y′(0)=y′(1)=0下,研究方程y″″(x)=f(x,y(x))的正解存在性,给出两端固定的弹性梁方程正解及多个正解存在的充分条件. 相似文献
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设p=5(mod 6)为素数.证明了丢番图方程χ^3一У^6=3pz^2。在p=5(mod 12)为素数时均无正整数解;在P=11(mod 12)为素数时均有无穷多组正整数解,并且还获得了该方程全部正整数解的通解公式,同时还给出了该方程的部分整数解. 相似文献
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Pierre Gaillard 《Journal of Nonlinear Modeling and Analysis》2022,4(4):615-627
Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order $n$ for any positive integer $n$, and we call these solutions, solutions of the order $n$. Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order $10$. 相似文献
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In this paper, we study the nonexistence and existence of positive solutions for the Kirchhoff type equation with nonlinearity having prescribed asymptotic behavior. Because of the structure of our equation, our nonexistence results have some special properties, and our conditions for positive solutions are also different from the existing results. 相似文献
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张瑾 《纯粹数学与应用数学》2009,25(4):786-788
研究一个包含伪Smarandache函数及其对偶函数方程的可解性,利用初等及组合方法给出了该方程的一系列正整数解,并证明了该方程的所有奇数解必为奇素数p(≥5)的方幂. 相似文献
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Existence of kink and unbounded traveling wave solutions of the Casimir equation for the Ito system 下载免费PDF全文
This paper study the traveling wave solutions of the Casimir equation for the Ito system. Since the derivative function of the wave function is a solution of a planar dynamical system, from which the exact parametric representations of solutions and bifurcations of phase portraits can be obtained. Thus, we show that corresponding to the compacton solutions of the derivative function system, there exist uncountably infinite kink wave solutions of the wave equation. Corresponding to the positive or negative periodic solutions and homoclinic solutions of the derivative function system, there exist unbounded wave solutions of the wave function equation. 相似文献
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设D是不能被3整除的正整数.本文证明了:当D>1012时,如果Pell方程U2-DV2=-1有解(U,V),则方程x2-D=3n至多有2组正整数解(x,n). 相似文献
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Giovany M. Figueiredo João R. Santos Júnior Antonio Suárez 《Israel Journal of Mathematics》2018,227(1):485-505
In this paper we study the existence, uniqueness and multiplicity of positive solutions to a non-linear Schr¨odinger equation. We describe the set of positive solutions. We use mainly the sub-supersolution method, bifurcation and variational arguments to obtain the results. 相似文献
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In this paper, by using global bifurcation theories we obtain some results for structure of positive solution set of some nonlinear equations with parameters. As a result, we obtain some existence results for positive solutions of the nonlinear operator equation. The main result can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinearities are positone. 相似文献
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设φ(n),S(n)分别表示正整数n的Euler函数和Smarandache函数,利用初等的方法和技巧,依据Smarandache函数计算公式,给出k的方程φ(p~αm)=S(p~(ακ))的所有解,其中p为素数,α,m为正整数且gcd(m,p)=1,由此得到方程φ(n)=S(n~k)的所有解(n,k)进而确定了满足条件S(n)|σ(n)的全部正整数n.最后,根据莫比乌斯变换反演定理证明了方程φ(n)=∑_(d|n)S(d)仅有两个解,分别为n=2~5和n=3×2~5. 相似文献