共查询到20条相似文献,搜索用时 140 毫秒
1.
2.
该文研究如下Kirchhoff型方程-(a+b∫R3 |▽u|2dx)Δu+V(x)u=|u|p-2U+ε|u|4u,x∈ R3,u∈ H1(R3),其中a>0,b>0,4<p<6,V(x)∈L3/2c(R3)是一个给定的非负函数且满足 lim V(x):=V∞.对V(x)给定适当的假设条件,当ε充分小时,证明了基态解... 相似文献
3.
《数学物理学报(A辑)》2016,(3)
该文研究全空间R~N上带权的半线性椭圆型方程-△u=|x|~α|u|~(p-1)u,x∈R~N与半空间R_+~N={x∈R~N:x_N0}上带权的半线性椭圆型问题-△u=|x|~α|u|~(p-1)u,x∈R_+~N,u|?R_+~N=0的Liouville型定理,其中N≥3,α-2.证明了,当1p(N+2α+2)/(N-2)时,上述问题的Morse指数有限的有界解只能是零解. 相似文献
4.
5.
Classification of positive solutions to an integral system with the poly-harmonic extension operator
In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R~+_n:{u(x)=c_n,a∫_?R_+~n(x_n~(1-a_v)(y)/|x-y|~(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n~(1-a_uθ)(x)/|x-y|~(n-a))dx,y∈ ?R_+~n,where n 2, 2-n a 1, κ, θ 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system. 相似文献
6.
7.
本文主要研究以下具临界增长的非线性p-Kirchhoff型方程的非平凡解的存在性:{-(a+b∫_(R~N)|▽u|~p)?_pu=|u|~(p*-2)u+μf (x)|u|~(q-2)u, x∈R~N,(0.1) u∈D~(1,p)(R~N),其中a≥0,b0,1pN,1qp,p*=N_p/(N-p),μ≥0,?_pu=div(|▽u|~(p-2)▽u)表示p-Laplace算子对函数u的作用, f∈L(p*/(p*-q))(R~N)\{0}且f是非负的.本文利用Ekeland变分原理和山路定理证明方程(0.1)在适当条件下至少存在两个非平凡解. 相似文献
8.
考虑如下Kirchhoff型问题{-(a+b∫RN︱▽u︱2dx)△u+V(x)u=f(x,u)u∈H1(RN)在RN上,通过山路引理,喷泉定理和对称山路引理得到问题非平凡解的存在性和多解性. 相似文献
9.
该文主要证明了以下非线Kirchhoff问题的单峰解的局部唯一性-(∈^2a+∈b∫R^3|▽u|^2dx)△u+u=K(x)|u|p-1u,u> 0,x∈R^3,其中∈>0任意小,a,b> 0,1
相似文献
10.
《数学物理学报(B辑英文版)》2015,(5)
In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {△2u- a+b∫R3|▽u|2dx △u+V(x)u=f(x, u), x∈ R3,u∈H2(R3),wherea, b 0 are constants and the primitive of the nonlinearityfis of superlinear growth near infinity inuand is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the AmbrosettiRabinowitz type condition. 相似文献
11.
Existence of ground state solutions for Kirchhoff‐type problems involving critical Sobolev exponents
《Mathematical Methods in the Applied Sciences》2018,41(1):371-385
In this paper, we study the existence of ground state solutions for a Kirchhoff‐type problem in involving critical Sobolev exponent. With the help of Nehari manifold and the concentration‐compactness principle, we prove that problem admits at least one ground state solution. 相似文献
12.
Ground state and nodal solutions for a class of biharmonic equations with singular potentials
下载免费PDF全文
![点击此处可从《Journal of Applied Analysis & Computation》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Hongliang Liu Qizhen Xiao Hongxia Shi Haibo Chen Zhisu Liu 《Journal of Applied Analysis & Computation》2019,9(4):1393-1406
In this paper, we are concerned with a class of fourth order elliptic equations of Kirchhoff type with singular potentials in $\mathbb{R}^{N}.$ The existence of ground state and nodal solutions are obtained by using variational methods and properties of Hessian matric. Furthermore, the "energy doubling" property of nodal solutions is also explored. 相似文献
13.
In this paper, we study the multiplicity results of positive solutions for a Kirchhoff type problem with critical growth, with the help of the concentration compactness principle, and we prove that problem admits two positive solutions, and one of the solutions is a positive ground state solution. 相似文献
14.
本文研究如下带有临界增长的分数阶Kirchhoff方程ε2sM(ε2s-3∫∫R3×R3-
|u(x)-u(y)|2/(x-y|3+2s|2dxdy)(-△)su+V(x)u = λW(x)f(u)+K(x)|u|2*s-2u,x ∈ R3,其中 M 是一个连续正的Kirchhoff函数,A>0是一个参数,3/4 < ... 相似文献
15.
We study an initial–boundary-value problem for a quasilinear thermoelastic plate of Kirchhoff & Love-type with parabolic heat conduction due to Fourier, mechanically simply supported and held at the reference temperature on the boundary. For this problem, we show the short-time existence and uniqueness of classical solutions under appropriate regularity and compatibility assumptions on the data. Further, we use barrier techniques to prove the global existence and exponential stability of solutions under a smallness condition on the initial data. It is the first result of this kind established for a quasilinear non-parabolic thermoelastic Kirchhoff & Love plate in multiple dimensions. 相似文献
16.
Jos Carlos de Albuquerque Yane Lísley Araújo Rodrigo Clemente 《Mathematical Methods in the Applied Sciences》2019,42(3):806-820
In this paper, we discuss the existence of bound and ground state solutions for a class of fractional Kirchhoff equations defined on the whole real line. The equation involves a nonlinear term with critical exponential growth in the Trudinger‐Moser sense. We deal with periodic and asymptotically periodic potential, which may change sign. We handle with the lack of compactness because of the unboundedness of the domain and the critical behavior of the nonlinearity. The main theorems are stated without the well‐known Ambrosetti‐Rabinowitz condition at infinity. 相似文献
17.
Paolo Caldiroli Roberta Musina 《Calculus of Variations and Partial Differential Equations》1999,8(4):365-387
We investigate the existence of ground state solutions to the Dirichlet problem in , u = 0 on , where , and is a domain in . In particular we prove that a non negative ground state solution exists when the domain is a cone, including the case . Moroever, we study the case of arbitrary domains, showing how the geometry of the domain near the origin and at infinity
affects the existence or non existence of ground state solutions.
Received April 16, 1998 / Accepted June 24, 1998 相似文献
18.
In this paper, we discuss the existence and uniqueness of solutions of the constrained variational problem with respect to the fractional Kirchhoff equation. For the exponent p<p*(s,N), a complete classification with respect to p for the existence of solutions of the fractional Kirchhoff functional on the L2-normalized manifold was given. Furthermore, all these solutions are unique up to translations, and our methods depend only on some simple energy estimates. 相似文献
19.
本文研究了一类Kirchhoff型方程。利用极大极小原理及惩罚函数方法,证明了上述方程变号解的存在性及集中性,我们的结果推广了文献[4]的结果。 相似文献
20.
在这篇文章, 我们研究了一分数阶基尔霍夫问题, 在一些适当的条件下, 得到了非平凡非负基态解的存在性. 相似文献