|
$
x'(t) + f(x'(t)) + g(t,x(t - \tau (t))) = p(t)
$
x'(t) + f(x'(t)) + g(t,x(t - \tau (t))) = p(t)
相似文献
2.
In this paper we deal with the four-point singular boundary value problem
|
$
\left\{ \begin{gathered}
(\phi _p (u'(t)))' + q(t)f(t,u(t),u'(t),u'(t)) = 0,t \in (0,1), \hfill \\
u'(0) - \alpha u(\xi ) = 0,u'(1) + \beta u(\eta ) = 0, \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
(\phi _p (u'(t)))' + q(t)f(t,u(t),u'(t),u'(t)) = 0,t \in (0,1), \hfill \\
u'(0) - \alpha u(\xi ) = 0,u'(1) + \beta u(\eta ) = 0, \hfill \\
\end{gathered} \right.
相似文献
3.
This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation
|
$
\left\{ \begin{gathered}
x'(t) = f(t,x(t),x(\alpha _1 (t)),...,x(\alpha _n (t)))fora.e.t \in [0,T], \hfill \\
\Delta x(t_k ) = I_k (x(t_k )),k = 1,...,m, \hfill \\
x(0) = x(T). \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
x'(t) = f(t,x(t),x(\alpha _1 (t)),...,x(\alpha _n (t)))fora.e.t \in [0,T], \hfill \\
\Delta x(t_k ) = I_k (x(t_k )),k = 1,...,m, \hfill \\
x(0) = x(T). \hfill \\
\end{gathered} \right.
相似文献
4.
Abstract. In this paper ,the oscillation criteria for the solutions of the nonlinear differential e-quations of neutral type of the forms: 相似文献
5.
The existence of at least one solution of the following multi-point boundary value problem
|
$
\left\{ \begin{gathered}
[\varphi (x'(t))]' = f(t,x(t),x'(t)),t \in (0,1), \hfill \\
x(0) - \sum\limits_{i = 1}^m {\alpha _i x'(\xi _i ) = 0,} \hfill \\
x'(1) - \sum\limits_{i = 1}^m {\beta _i x(\xi _i ) = 0} \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
[\varphi (x'(t))]' = f(t,x(t),x'(t)),t \in (0,1), \hfill \\
x(0) - \sum\limits_{i = 1}^m {\alpha _i x'(\xi _i ) = 0,} \hfill \\
x'(1) - \sum\limits_{i = 1}^m {\beta _i x(\xi _i ) = 0} \hfill \\
\end{gathered} \right.
相似文献
6.
We establish asymptotic formulas for nonoscillatory solutions of a special conditionally oscillatory half-linear second order
differential equation, which is seen as a perturbation of a general nonoscillatory half-linear differential equation
|
$
(r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x) = |x|^{p - 1} \operatorname{sgn} x,p > 1,
$
(r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x) = |x|^{p - 1} \operatorname{sgn} x,p > 1,
相似文献
7.
We establish conditions under which Baire measurable solutions f of
|
$
\Gamma (x,y,|f(x) - f(y)|) = \Phi (x,y,f(x + \phi _1 (y)),...,f(x + \phi _N (y)))
$
\Gamma (x,y,|f(x) - f(y)|) = \Phi (x,y,f(x + \phi _1 (y)),...,f(x + \phi _N (y)))
相似文献
8.
In this paper, solutions for two types of ultrametric kinetic equations of the form reaction-diffusion are obtained and properties
of these solutions are investigated. General method to find the solution of equation of the form
|
$
\tfrac{\partial }
{{\partial t}}f(x,t) = \int_{\mathbb{Q}_p } {W(|x - y|_p )(f(y,t) - f(x,t))dy + V(|x|_p )f(x,t),f(x,0) = \phi (|x|_p ),}
$
\tfrac{\partial }
{{\partial t}}f(x,t) = \int_{\mathbb{Q}_p } {W(|x - y|_p )(f(y,t) - f(x,t))dy + V(|x|_p )f(x,t),f(x,0) = \phi (|x|_p ),}
相似文献
9.
This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type(φ(x'(t)))' q(t)f(t,x(t),x'(t)) = 0, t ∈ (0, 1),subject to the following boundary condition:a1φ(x(0)) - a2φ(x'(0)) = 0, a3φ(x(1)) a4φ(x'(1)) = 0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem,sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly. 相似文献
10.
In this paper, we study the existence of periodic solutions of Rayleigh equation
|
$
x' + f(x') + g(x) = p(t)
$
x' + f(x') + g(x) = p(t)
相似文献
11.
Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point
boundary value problem at resonance
|
$\begin{gathered}
x^{(n)} (t) = f(t,x(t),x'(t),...,x^{(n - 1)} (t)),t \in (0,1), \hfill \\
x(0) = \sum\limits_{i = 1}^m {a_i x(\xi _i ),x'(0) = ... = x^{(n - 2)} (0) = 0,x^{(n - 1)} (1) = } \sum\limits_{j = 1}^l {\beta _j x^{(n - 1)} (\eta _j )} , \hfill \\
\end{gathered}
$\begin{gathered}
x^{(n)} (t) = f(t,x(t),x'(t),...,x^{(n - 1)} (t)),t \in (0,1), \hfill \\
x(0) = \sum\limits_{i = 1}^m {a_i x(\xi _i ),x'(0) = ... = x^{(n - 2)} (0) = 0,x^{(n - 1)} (1) = } \sum\limits_{j = 1}^l {\beta _j x^{(n - 1)} (\eta _j )} , \hfill \\
\end{gathered}
相似文献
12.
Some new oscillation criteria are established for the nonlinear damped differential equation
|
( x,x' ) )^ + p( t )k_2( x,x' )x' + q( t )f( x( t ) ) = 0,t t_0.{\left( {r\left( t \right){k_1}\left( {x,x'} \right)} \right)^\prime } + p\left( t \right){k_2}\left( {x,x'} \right)x' + q\left( t \right)f\left( {x\left( t \right)} \right) = 0,\;t \ge {t_0}. 相似文献
13.
The nonhomogeneous backward Cauchy problem
|
$
u_t + Au(t) = f(t),u(T) = \phi
$
u_t + Au(t) = f(t),u(T) = \phi
相似文献
14.
We study oscillatory properties of solutions of the Emden-Fowler type differential equation
|
$
u^{(n)} (t) + p(t)|u(\sigma (t))|^\lambda signu(\sigma (t)) = 0,
$
u^{(n)} (t) + p(t)|u(\sigma (t))|^\lambda signu(\sigma (t)) = 0,
相似文献
15.
In this paper, oscillatory and asymptotic properties of solutions of nonlinear fourth order neutral dynamic equations of the form $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = 0(H)$ and $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = f(t),(NH)$ are studied on a time scale $\mathbb{T}$ under the assumption that $\int\limits_{t_0 }^\infty {\tfrac{t} {{r(t)}}\Delta t = \infty } $ and for various ranges of p( t). In addition, sufficient conditions are obtained for the existence of bounded positive solutions of the equation (NH) by using Krasnosel’skii’s fixed point theorem. 相似文献
16.
Let $
\mathbb{B}
$
\mathbb{B}
be the unit ball in ℂ
n
and let H($
\mathbb{B}
$
\mathbb{B}
) be the space of all holomorphic functions on $
\mathbb{B}
$
\mathbb{B}
. We introduce the following integral-type operator on H($
\mathbb{B}
$
\mathbb{B}
):
|
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
相似文献
17.
The singular boundary value problems of third-order differential equations
|
$
{*{20}c}
{ - u'(t) = h(t)f(t,u(t)), t \in (0,1),} \\
{u(0) = u'(0) = 0, u'(1) = \alpha u'(\eta )} \\
$
\begin{array}{*{20}c}
{ - u'(t) = h(t)f(t,u(t)), t \in (0,1),} \\
{u(0) = u'(0) = 0, u'(1) = \alpha u'(\eta )} \\
\end{array}
相似文献
18.
This work is a continuation of paper [1], where was considered analog of the problem of the first return for ultrametric diffusion.
The main result of this paper consists in construction and investigation of stochastic quantity $
\tau _{B_r (a)}
$
\tau _{B_r (a)}
( ω), which has meaning of the first passage time into domain B
r
( a) by trajectories of the Markov stochastic process ζ( t, ω).Markov stochastic process is given by distribution density f( x, t), x ∈ ℚ
p
, t ∈ R
+, which is solution of the Cauchy problem
|
$
\frac{\partial }
{{\partial t}}f(x,t) = - D_x^\alpha f(x,t),f(x,0) = \Omega (\left| x \right|_p ).
$
\frac{\partial }
{{\partial t}}f(x,t) = - D_x^\alpha f(x,t),f(x,0) = \Omega (\left| x \right|_p ).
相似文献
19.
In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\left\{ \begin{gathered} (\phi _p (u\prime ))\prime + q(t)f(t, u) = 0,0< t< 1, \hfill \\ u(0) - B(u\prime (\eta )) = 0, u\prime (1) = 0 \hfill \\ \end{gathered} \right.$$ and $$\left\{ \begin{gathered} (\phi _p (u\prime ))\prime + q(t)f(t, u) = 0,0< t< 1, \hfill \\ u\prime (0) = 0, u(1) + B(u\prime (\eta )) = 0 \hfill \\ \end{gathered} \right.$$ The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0,1. 相似文献
20.
In this paper, we establish sufficient conditions to guarantee the existence of at least three or 2 n − 1 positive solutions of nonlocal boundary value problems consisting of the second-order differential equation with p-Laplacian and one of following boundary conditions and Examples are presented to illustrate the main results.
Supported by National Natural Science Foundation of P. R. China (No: 10371006). 相似文献
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