共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we study the existence of nodal solutions for the following problem:-(φ_p(x′))′= α(t)φ_p(x~+) + β(t)φ_p(x~-) + ra(t)f(x), 0 t 1,x(0) = x(1) = 0,where φ_p(s) = |s|~(p-2)s, a ∈ C([0, 1],(0, ∞)), x~+= max{x, 0}, x~-=- min{x, 0}, α(t), β(t) ∈C[0, 1]; f ∈ C(R, R), sf(s) 0 for s ≠ 0, and f_0, f_∞∈(0, ∞), where f_0 = lim_|s|→0f(s)/φ_p(s), f_∞ = lim|s|→+∞f(s)/φ_p(s).We use bifurcation techniques and the approximation of connected components to prove our main results. 相似文献
2.
On ground state of fractional $p$-Kirchhoff equation involving subcritical and critical exponential growth 下载免费PDF全文
In this paper, we concern the existence of nontrivial ground state solutions of
fractional $p$-Kirchhoff equation
$$\left\{\begin{array}{ll}
m\left(\|u\|^p\right) [(-\Delta)_p^su+V(x)|u|^{p-2}u]
=f(x,u) \quad\text{in}\, \mathbb{R}^N, \vspace{0.2
cm}\\ \|u\|=\left(\int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy +\int_{\mathbb{R}^N}V(x)|u|^pdx\right)^{\frac{1}{p}},
\end{array}\right.$$
where $m:[0,+\infty)\rightarrow [0,+\infty)$ is a continuous function, $(-\Delta)_p^s$ is the fractional $p$-Laplacian operator with $0相似文献
3.
In this paper,we are interested in the existence of positive solutions for the Kirchhoff type problems{-(a_1 + b_1M_1(∫_?|▽u|~pdx))△_(_pu) = λf(u,v),in ?,-(a_2 + b_2M_2(∫?|▽v|~qdx))△_(_qv) = λg(u,v),in ?,u = v = 0,on ??,where 1 p,q N,M i:R_0~+→ R~+(i = 1,2) are continuous and increasing functions.λ is a parameter,f,g ∈ C~1((0,∞) ×(0,∞)) × C([0,∞) × [0,∞)) are monotone functions such that f_s,f_t,g_s,g_t ≥ 0,and f(0,0) 0,g(0,0) 0(semipositone).Our proof is based on the sub-and super-solutions techniques. 相似文献
4.
The purpose of this article is to study the existence and uniqueness of global solution for the nonlinear hyperbolic-parabolic equation of Kirchhoff-Carrier type: $$ u_{tt} + \mu u_t - M\left (\int _{\Omega _t}|\nabla u|^2dx\right )\Delta u = 0\quad \hbox {in}\ \Omega _t\quad \hbox {and}\quad u|_{\Gamma _t} = \dot \gamma $$ where $ \Omega _t = \{x\in {\shadR}^2 | \ x = y\gamma (t), \ y\in \Omega \} $ with boundary o t , w is a positive constant and n ( t ) is a positive function such that lim t M X n ( t ) = + X . The real function M is such that $ M(r) \geq m_0 \gt 0 \forall r\in [0,\infty [ $ . 相似文献
5.
Zhou Dingxuan 《数学年刊B辑(英文版)》1991,12(4):525-530
Let {L_n}_(n∈s) be positive linear operators in L_(I), I=[0, 1] or [0, ∞). This paper considers their variants in L_p(I×I)L_(n,m)(F; x, y)=L_n(L_m(F(u, v); y); x)=L_m(L_n(F(u, v); x); y), n, m∈N.The characterization problem for these operators is solved which gives the inverse theorems in L_p for multidimensional Bernstein type operators. 相似文献
6.
Chen Yunmei 《数学年刊B辑(英文版)》1987,8(4):498-522
This paper deals with the following IBV problem of nonlinear parabolic equation:
$$\[\left\{ {\begin{array}{*{20}{c}}
{{u_t} = \Delta u + F(u,{D_x}u,D_x^2u),(t,x) \in {B^ + } \times \Omega ,}\{u(0,x) = \varphi (x),x \in \Omega }\{u{|_{\partial \Omega }} = 0}
\end{array}} \right.\]$$
where $\[\Omega \]$ is the exterior domain of a compact set in $\[{R^n}\]$ with smooth boundary and F satisfies $\[\left| {F(\lambda )} \right| = o({\left| \lambda \right|^2})\]$, near $\[\lambda = 0\]$. It is proved that when $\[n \ge 3\]$, under the suitable smoothness and compatibility conditions, the above problem has a unique global smooth solution for small initial data. Moreover, It is also proved that the solution has the decay property $\[{\left\| {u(t)} \right\|_{{L^\infty }(\Omega )}} = o({t^{ - \frac{n}{2}}})\]$, as $\[t \to + \infty \]$. 相似文献
7.
We study existence of positive weak solution for a class of $p$-Laplacian problem $$\left\{\begin{array}{ll}-\Delta_{p}u = \lambda g(x)[f(u)-\frac{1}{u^{\alpha}}], & x\in \Omega,\\u= 0 , & x\in\partial \Omega,\end{array\right.$$ where $\lambda$ is a positive parameter and $\alpha\in(0,1),$ $\Omega $ is a bounded domain in $ R^{N}$ for $(N > 1)$ with smooth boundary, $\Delta_{p}u = div (|\nabla u|^{p-2}\nabla u)$ is the p-Laplacian operator for $( p > 2),$ $g(x)$ is $C^{1}$ sign-changing function such that maybe negative near the boundary and be positive in the interior and $f$ is $C^{1}$ nondecreasing function $\lim_{s\to\infty}\frac{f(s)}{s^{p-1}}=0.$ We discuss the existence of positive weak solution when $f$ and $g$ satisfy certain additional conditions. We use the method of sub-supersolution to establish our result. 相似文献
8.
奇异非线性$p-$调和方程的一类正整体解 总被引:2,自引:0,他引:2
设p>1,β≥0是常数, n是自然数, 是一个连续函数.本文研究形如的奇异非线性p-调和方程的正整体解,给出了该类方程具有无穷多个其渐近阶刚好为|x|(2n-2)(当|x|→∞时)的径向对称的正整体解的若干充分条件. 相似文献
9.
In this paper, the authors give the local L~2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equations(~*) along a curve γ:■where φ : R~+→R satisfies some suitable conditions and φ((-?)~(1/2)) is a pseudo-differential operator with symbol φ(|ξ|). As a consequence of the above result, the authors give the pointwise convergence of the solution(when n = 1) of the equation(~*) along curve γ.Moreover, a global L~2 estimate of the maximal operator S_(φ,γ)~* is also given in this paper. 相似文献
10.
《复变函数与椭圆型方程》2012,57(8):727-729
Let T ( f ) and N ( r,c ) denote the usual Nevanlinna characteristic and the counting function for the c -points of a meromorphic function f , respectively. Using a result of Miles and Shea ( Quart. J. Math. Oxford , 24 (2), (1973), 377-383) and two simple estimates for trigonometric functions, we show in connection with a 1929 problem of Nevanlinna for meromorphic functions f of finite order 1 < u < X $$ \limsup\limits_{r\rightarrow \infty } { N(r, 0)+N(r, \infty ) \over T(r, \,f)}\ge {2\sqrt 2 \over \pi} {|\sin \pi \lambda | \over D(\lambda )}\ge (0.9)\, {{|\sin \pi \lambda | \over {D(\lambda )}, }} $$ with D ( u ) = q +|sin ~ u | for $ q\le \lambda \le q + \fraca {1}{2} $ and D ( u ) = q + 1 for $ q + {\fraca {1} {2}} \le \lambda \lt q + 1 $ , where $ q = \lfloor \lambda \rfloor $ . 相似文献
11.
Let $\Omega \subset \Bbb{R}^2$ denote a bounded domain whose boundary
$\partial \Omega$ is Lipschitz and contains a segment $\Gamma_0$ representing
the austenite-twinned martensite interface. We prove
$$\displaystyle{\inf_{{u\in \cal W}(\Omega)} \int_\Omega \varphi(\nabla
u(x,y))dxdy=0}$$ for any elastic energy density $\varphi : \Bbb{R}^2
\rightarrow [0,\infty)$ such that $\varphi(0,\pm 1)=0$. Here
${\cal W}(\Omega)$ consists of all Lipschitz functions $u$ with
$u=0$ on $\Gamma_0$ and $|u_y|=1$ a.e. Apart from the trivial case
$\Gamma_0 \subset \reel \times \{a\},~a\in \Bbb{R}$, this result is
obtained through the construction of suitable minimizing sequences
which differ substantially for vertical and non-vertical
segments. 相似文献
12.
Shi Jihuai 《中国科学A辑(英文版)》1998,41(1):22-32
A necessary and sufficient condition for the boundedness of the operator: $(T_{s,u,u} f)(\xi ) = h^{u + \tfrac{v}{a}} (\xi )\smallint _{\Omega _a } h^s (\xi ')K_{s,u,v} (\xi ,\xi ')f(\xi ')dv(\xi ') on L^p (\Omega _a ,dv_\lambda ),1< p< \infty $ , is obtained, where $\Omega _a = \left\{ {\xi = (z,w) \in \mathbb{C}^{n + m} :z \in \mathbb{C}^n ,w \in \mathbb{C}^m ,|z|^2 + |w|^{2/a}< 1} \right\},h(\xi ) = (1 - |z|^2 )^a - |w|^2 $ andK x,u,v (ξ,ξ′).This generalizes the works in literature from the unit ball or unit disc to the weakly pseudoconvex domain ω a . As an appli cation, it is proved thatf?L H p (ω a ,dv λ) implies $h\tfrac{{|a|}}{a} + |\beta |(\xi )D_2^a D_z^\beta f \in L^p (\Omega _a ,dv_\lambda ),1 \leqslant p< \infty $ , for any multi-indexa=(α1,?,α n and ß = (ß1, —ß). An interesting question is whether the converse holds. 相似文献
13.
In the present paper, we consider the following stochastic control problem: to minimize the average expected total cost $$J(x,u) = \mathop {\lim \inf }\limits_{T \to \infty } (1/T)E_x^u \int_0^T {\left[ {\phi (\xi _t ) + |u_t (\xi )|} \right]} dt,$$ 〈subject to $$d\xi _t = u_1 (\xi )dt + dw_t , \xi _0 = x, |u| \leqslant 1,$$ (w t) a Wiener process, with all measurable functions on the past of the state process {ξ s ;s≤t} and bounded by unity, admissible as controls. It is proved that, under very mild conditions on the running cost function φ(·), the optimal law is of the form $$\begin{gathered} u_t^* (\xi ) = - sign\xi _t , |\xi _t | > b, \hfill \\ u_t^* (\xi ) = 0, |\xi _t | > b. \hfill \\ \end{gathered} $$ The cutoff pointb and the performance rate of the optimal lawu* are simultaneously determined in terms of the function φ(·) through a simple system of integrotranscendental equations. 相似文献
14.
This paper deals with the existence of solutions for the problem
{(Фp(u′))′=f(t,u,u′),t∈(0,1),
u′(0)=0,u(1)=∑i=1^n-2aiu(ηi),
where Фp(s)=|s|^p-2s,p〉1.0〈η1〈η2〈…〈ηn-2〈1,ai(i=1,2,…,n-2)are non-negative constants and ∑i=1^n-2ai=1.Some known results are improved under some sign and growth conditions. The proof is based on the Brouwer degree theory. 相似文献
{(Фp(u′))′=f(t,u,u′),t∈(0,1),
u′(0)=0,u(1)=∑i=1^n-2aiu(ηi),
where Фp(s)=|s|^p-2s,p〉1.0〈η1〈η2〈…〈ηn-2〈1,ai(i=1,2,…,n-2)are non-negative constants and ∑i=1^n-2ai=1.Some known results are improved under some sign and growth conditions. The proof is based on the Brouwer degree theory. 相似文献
15.
研究拟线性椭圆系统(?)的非平凡非负解或正解的多重性,这里Ω(?)R~N是具有光滑边界(?)Ω的有界域,1≤q
p~*/p~*-q,其中当N≤p时,p~*=+∞,而当1
相似文献
16.
Yongtao Jing & Zhaoli Liu 《数学研究》2015,48(3):290-305
Let $1
0.$ This is in sharp contrast to D'Aprile and Mugnai's non-existence results. 相似文献
17.
Benboubker Mohamed Badr Hjiaj Hassan OUARO Stanislas 《Journal of Applied Analysis & Computation》2014,4(3):245-270
In this work, we give an existence result of entropy solutions for nonlinear anisotropic elliptic equation of the type $$- \mbox{div} \big( a(x,u,\nabla u)\big)+ g(x,u,\nabla u) + |u|^{p_{0}(x)-2}u = f-\mbox{div} \phi(u),\quad \mbox{ in } \Omega,$$ where $-\mbox{div}\big(a(x,u,\nabla u)\big)$ is a Leray-Lions operator, $\phi \in C^{0}(I\!\!R,I\!\!R^{N})$. The function $g(x,u,\nabla u)$ is a nonlinear lower order term with natural growth with respect to $|\nabla u|$, satisfying the sign condition and the datum $f$ belongs to $L^1(\Omega)$. 相似文献
18.
Dong Guangchang 《数学年刊B辑(英文版)》1986,7(3):277-302
In this paper, the author proves the existence and uniqueness of nonnegative solution for the first boundary value problem of uniform degenerated parabolic equation
$$\[\left\{ {\begin{array}{*{20}{c}}
{\frac{{\partial u}}{{\partial t}} = \sum {\frac{\partial }{{\partial {x_i}}}\left( {v(u){A_{ij}}(x,t,u)\frac{{\partial u}}{{\partial {x_j}}}} \right) + \sum {{B_i}(x,t,u)} \frac{{\partial u}}{{\partial {x_i}}}} + C(x,t,u)u\begin{array}{*{20}{c}}
{}&{(x,t) \in [0,T]}
\end{array},}\{u{|_{t = 0}} = {u_0}(x),x \in \Omega ,}\{u{|_{x \in \partial \Omega }} = \psi (s,t),0 \le t \le T}
\end{array}} \right.\]$$
$$\[\left( {\frac{1}{\Lambda }{{\left| \alpha \right|}^2} \le \sum {{A_{ij}}{\alpha _i}{\alpha _j}} \le \Lambda {{\left| \alpha \right|}^2},\forall a \in {R^n},0 < \Lambda < \infty ,v(u) > 0\begin{array}{*{20}{c}}
{and}&{v(u) \to 0\begin{array}{*{20}{c}}
{as}&{u \to 0}
\end{array}}
\end{array}} \right)\]$$
under some very weak restrictions, i.e. $\[{A_{ij}}(x,t,r),{B_i}(x,t,r),C(x,t,r),\sum {\frac{{\partial {A_{ij}}}}{{\partial {x_j}}}} ,\sum {\frac{{\partial {B_i}}}{{\partial {x_i}}} \in \overline \Omega } \times [0,T] \times R,\left| {{B_i}} \right| \le \Lambda ,\left| C \right| \le \Lambda ,\],\[\left| {\sum {\frac{{\partial {B_i}}}{{\partial {x_i}}}} } \right| \le \Lambda ,\partial \Omega \in {C^2},v(r) \in C[0,\infty ).v(0) = 0,1 \le \frac{{rv(r)}}{{\int_0^r {v(s)ds} }} \le m,{u_0}(x) \in {C^2}(\overline \Omega ),\psi (s,t) \in {C^\beta }(\partial \Omega \times [0,T]),0 < \beta < 1\],\[{u_0}(s) = \psi (s,0).\]$ 相似文献
19.
S. H. Rasouli & H. Norouzi 《偏微分方程(英文版)》2015,28(1):1-8
We prove the existence of positive solutions for the system$$\begin{align*}\begin{cases}-\Delta_{p} u =\lambda a(x){f(v)}{u^{-\alpha}},\qquad x\in \Omega,\\-\Delta_{q} v = \lambda b(x){g(u)}{v^{-\beta}},\qquad x\in \Omega,\\u = v =0, \qquad x\in\partial \Omega,\end{cases}\end{align*}$$where $\Delta_{r}z={\rm div}(|\nabla z|^{r-2}\nabla z)$, for $r>1$ denotes the r-Laplacian operator and $\lambda$ is a positive parameter, $\Omega$ is a bounded domain in $\mathbb{R}^{n}$, $n\geq1$ with sufficiently smooth boundary and $\alpha, \beta \in (0,1).$ Here $ a(x)$ and $ b(x)$ are $C^{1}$ sign-changingfunctions that maybe negative near the boundary and $f,g $ are $C^{1}$ nondecreasing functions, such that $f, g :\ [0,\infty)\to [0,\infty);$ $f(s)>0,$ $g(s)>0$ for $s> 0$, $\lim_{s\to\infty}g(s)=\infty$ and$$\lim_{s\to\infty}\frac{f(Mg(s)^{\frac{1}{q-1}})}{s^{p-1+\alpha}}=0,\qquad \forall M>0.$$We discuss the existence of positive weak solutions when $f$, $g$, $a(x)$ and $b(x)$ satisfy certain additional conditions. We employ the method of sub-supersolution to obtain our results. 相似文献
20.
Multiple solutions for a nonhomogeneous Schrodinger-Poisson system with concave and convex nonlinearities 下载免费PDF全文
In this paper, we consider the following nonhomogeneous Schrodinger-Poisson equation
$$
\left\{
- \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\\ \Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3,
\right.
$$
where $1
相似文献