|
$
x' + q(t)x'(t) - r(t)f(x(\phi (t))) = 0,
$
x' + q(t)x'(t) - r(t)f(x(\phi (t))) = 0,
相似文献
2.
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
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.
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
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.
The objective of this paper is to study asymptotic properties of the third-order neutral differential equation
|
$
\left[ {a\left( t \right)\left( {\left[ {x\left( t \right) + p\left( t \right)x\left( {\sigma \left( t \right)} \right)} \right]^{\prime \prime } } \right)^\gamma } \right]^\prime + q\left( t \right)f\left( {x\left[ {\tau \left( t \right)} \right]} \right) = 0, t \geqslant t_0 . \left( E \right)
$
\left[ {a\left( t \right)\left( {\left[ {x\left( t \right) + p\left( t \right)x\left( {\sigma \left( t \right)} \right)} \right]^{\prime \prime } } \right)^\gamma } \right]^\prime + q\left( t \right)f\left( {x\left[ {\tau \left( t \right)} \right]} \right) = 0, t \geqslant t_0 . \left( E \right)
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.
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
10.
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
11.
In this paper we consider the bifurcation problem -div A（x, u）=λa（x）｜u｜^p-2u＋f（x,u,λ） in Ω with p 〉 1.Under some proper assumptions on A（x,ξ）,a（x） and f（x,u,λ）,we show that the existence of an unbounded branch of positive solutions bifurcating Irom the principal eigenvalue of the problem --div A（x, u）=λa（x）｜u｜^p-2u. 相似文献
12.
In this paper we apply the method of potentials for studying the Dirichlet and Neumann boundary-value problems for a B-elliptic equation in the form
|
$
\Delta _{x'} u + B_{x_{p - 1} } u + x_p^{ - \alpha } \frac{\partial }
{{\partial x_p }}\left( {x_p^\alpha \frac{{\partial u}}
{{\partial x_p }}} \right) = 0
$
\Delta _{x'} u + B_{x_{p - 1} } u + x_p^{ - \alpha } \frac{\partial }
{{\partial x_p }}\left( {x_p^\alpha \frac{{\partial u}}
{{\partial x_p }}} \right) = 0
相似文献
13.
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）. This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）. 相似文献
14.
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
15.
Employing the coincidence degree theory of Mawhin we obtain some existence results of periodic solutions for a type of neutral Rayleigh equation with variable parameter $$((x(t) - c(t)x(t - \tau))'' + f(x'(t)) + g(x(t - \gamma(t))) = e(t).$$ It is worth noting that c( t) is no longer a constant which is different from the corresponding ones of past work. Furthermore, our results generalize corresponding work in the past. 相似文献
16.
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
17.
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
18.
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
19.
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
20.
Denote by B(τ) the class of all complex functions of the form
|
$
f(z) \equiv \tau + \sum\limits_{n = 1}^\infty {(a_n (f)z^n + \overline {b_n (f)} \bar z^n )}
$
f(z) \equiv \tau + \sum\limits_{n = 1}^\infty {(a_n (f)z^n + \overline {b_n (f)} \bar z^n )}
相似文献
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