共查询到20条相似文献,搜索用时 62 毫秒
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In this paper we consider the weakly coupled elliptic system with critical growth
where a, b, c, d are C
1-functions defined in a bounded regular domain of
N
. Here we construct families of solutions which blow-up and concentrate at some points in as the positive parameter goes to zero.*The authors are supported by M.I.U.R., project Metodi variazionali e topologici nello studio di fenomeni non lineari. 相似文献
3.
The Existence of Solutions of Elliptic Equations
with Neumann Boundary Condition for Superlinear Problems 总被引:1,自引:0,他引:1
ChongLI 《数学学报(英文版)》2004,20(6):965-976
In this paper, we study and discuss the existence of multiple solutions of a class of non-linear elliptic equations with Neumann boundary condition, and obtain at least seven non-trivial solutions in which two are positive, two are negative and three are sign-changing. The study of problem (1.1):{-△u αu=f(u),x∈Ω, x∈Ω,δu/δr=0,x∈δΩ,is based on the variational methods and critical point theory. We form our conclusion by using the sub-sup solution method, Mountain Pass Theorem in order intervals, Leray-Schauder degree theory and the invariance of decreasing flow. 相似文献
4.
Zhi Wen DUAN Kwang Ik KIM 《数学学报(英文版)》2007,23(6):1083-1094
This paper is concerned with a nonlocal hyperbolic system as follows utt = △u + (∫Ωvdx )^p for x∈R^N,t〉0 ,utt = △u + (∫Ωvdx )^q for x∈R^N,t〉0 ,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N, where 1≤ N ≤3, p ≥1, q ≥ 1 and pq 〉 1. Here the initial values are compactly supported and Ω belong to R^N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed. 相似文献
5.
The initial boundary value problem
$ {*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ $ \begin{array}{*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ \end{array} 相似文献
6.
Shuang-jie Peng 《应用数学学报(英文版)》2006,22(1):137-162
Abstract Let Ω be the unit ball centered at the origin in
. We study the following problem
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In this paper, we study the Pohozaev identity associated with a Henon-Lane-Emden system involving the fractional Laplacian:■in a star-shaped and bounded domain Ω for s ∈(0,1). As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases. 相似文献
8.
Existence Results for Superlinear Elliptic Equations with Nonlinear Boundary Value Conditions 下载免费PDF全文
Xiao Hui Yu 《数学学报(英文版)》2019,35(10):1655-1680
In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition
$$\left\{ {\begin{array}{*{20}{c}}
{ - \Delta u + u = {{\left| u \right|}^{r - 2}}u}&{in\;\Omega ,\;\;} \\
{\frac{{\partial u}}{{\partial v}} = {{\left| u \right|}^{q - 2}}u}&{on\;\partial \Omega ,}
\end{array}} \right.$$
where Ω ⊂ ℝN, N ≥ 3 is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases: (i) Both q and r are subcritical; (ii) r is critical and q is subcritical; (iii) r is subcritical and q is critical; (iv) Both q and r are critical. 相似文献
9.
Xiu Hui YANG Fu Cai LI Chun Hong XIE 《数学学报(英文版)》2005,21(4):923-928
Abstract In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions: {ut-a(u, v)△u=g(u, v), vt-b(u, v)△v=h(u, v), δu/δη=d(u, v), δu/δη=f(u, v).Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques. 相似文献
10.
We consider the ( p , n m p ) right focal boundary value problem: $${\matrix{{(- 1)^{n - p} u^{(n)} \! = \lambda \;f(t, u), } \hfill & \ {{\rm for }\ 0 \lt t \lt 1, } \hfill \cr \quad \quad \,{u^{(i)} (0) = 0, } \hfill & {0 \le i \le p - 1, } \hfill \cr \quad \quad \,{u^{(i)} (1) = 0, } \hfill & {p \le i \le n - 1, } \hfill \cr}} $$ where 1 h p h n m 1 is fixed and u > 0. Using a fixed point theorem for operators on a cone, we develop criteria for the existence of positive solutions of the boundary value problem for u on a suitable interval. 相似文献
11.
Convergence to Diffusion Waves for Nonlinear Evolution Equations with Ellipticity and Damping, and with Different End States 总被引:1,自引:0,他引:1
Chang Jiang ZHU Zhi Yong ZHANG Hui YIN 《数学学报(英文版)》2006,22(5):1357-1370
In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects: {ψt=-(1-α)ψ-θx+αψxx, θt=-(1-α)θ+νψx+(ψθ)x+αθxx(E) with initial data (ψ,θ)(x,0)=(ψ0(x),θ0(x))→(ψ±,θ±)as x→±∞ where α and ν are positive constants such that α 〈 1, ν 〈 4α(1 - α). Under the assumption that |ψ+ - ψ-| + |θ+ - θ-| is sufficiently small, we show the global existence of the solutions to Cauchy problem (E) and (I) if the initial data is a small perturbation. And the decay rates of the solutions with exponential rates also are obtained. The analysis is based on the energy method. 相似文献
12.
Massimo Grossi 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(2):227-241
Let Ω be a smooth bounded domain of
with N ≥ 5. In this paper we prove, for ɛ > 0 small, the nondegeneracy of the solution of the problem
13.
Patrick Winkert 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(3):289-302
In this paper we prove the L
∞-boundedness of solutions of the quasilinear elliptic equation
|