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1.
By means of Mawhin’s continuation theorem, a class of p-Laplacian type differential equation with a deviating argument of the form
is studied. A new result, related to β(t) and the deviating argument τ(t,|x|∞), is obtained. It is significant that the growth degree with respect to the variable x in g(t,x) is allowed to be greater than p−1, which could be achieved infrequently in previous papers. 相似文献
(φp(x′(t)))′+f(x(t))x′(t)+β(t)g(t,x(t−τ(t,|x|∞)))=e(t)
2.
In this paper, a higher order p-Laplacian neutral functional differential equation with a deviating argument:
[φp([x(t)−c(t)x(t−σ)](n))](m)+f(x(t))x′(t)+g(t,x(t−τ(t)))=e(t) 相似文献
3.
In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Liénard type p-Laplacian equation with a deviating argument of the form:
相似文献
(?p(x′(t)))′+f(x(t))x′(t)+g(t,x(t-τ(t)))=e(t).
4.
By using topological degree theory and some analysis skill, we obtain sufficient conditions for the existence and uniqueness of periodic solutions for Liénard type p-Laplacian differential equation. 相似文献
5.
As p-Laplacian equations have been widely applied in the field of fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Lu’s continuation theorem, which is an extension of Manásevich-Mawhin, we study the existence of periodic solutions for a Rayleigh type p-Laplacian equation
(φp(x′(t)))′+f(x′(t))+g1(x(t-τ1(t,|x|∞)))+β(t)g2(x(t-τ2(t,|x|∞)))=e(t). 相似文献
6.
The existence and uniqueness of periodic solutions for a kind of Duffing-type equation with two deviating arguments 总被引:1,自引:0,他引:1
By applying Mawhin’s continuation theorem and establishing new lemmas, some sufficient conditions for the existence and uniqueness of periodic solutions were obtained for a Duffing-type equation with two deviating arguments. Moreover, an example is given to illustrate the results. 相似文献
7.
Lijuan Wang Jianying Shao Hua Meng Bing Xiao Fei Long 《Journal of Computational and Applied Mathematics》2009
In this paper, the Liénard type p-Laplacian equation with two deviating arguments
is studied. By applying the coincidence degree theory, we obtain some new results on the existence of periodic solutions to this equation. Our results improve and extend some existing ones in the literature. 相似文献
(φp(x′(t)))′+f(x(t))x′(t)+g1(t,x(t−τ1(t)))+g2(t,x(t−τ2(t)))=e(t)
8.
9.
By using topological degree theory and some analysis skills, we obtain some sufficient conditions for the existence and uniqueness of periodic solutions for a class of forced generalized Liénard systems. 相似文献
10.
Existence of periodic solutions for a kind of Rayleigh equation with a deviating argument
is studied, and some new results are obtained. Our work generalizes and improves the known results in the literature. 相似文献
x″(t)+f(x′(t))+g(t,x(t−τ(t)))=p(t)
11.
Goro Akagi 《Journal of Differential Equations》2007,241(2):359-385
The existence of local (in time) solutions of the initial-boundary value problem for the following degenerate parabolic equation: ut(x,t)−Δpu(x,t)−|u|q−2u(x,t)=f(x,t), (x,t)∈Ω×(0,T), where 2?p<q<+∞, Ω is a bounded domain in RN, is given and Δp denotes the so-called p-Laplacian defined by Δpu:=∇⋅(|∇u|p−2∇u), with initial data u0∈Lr(Ω) is proved under r>N(q−p)/p without imposing any smallness on u0 and f. To this end, the above problem is reduced into the Cauchy problem for an evolution equation governed by the difference of two subdifferential operators in a reflexive Banach space, and the theory of subdifferential operators and potential well method are employed to establish energy estimates. Particularly, Lr-estimates of solutions play a crucial role to construct a time-local solution and reveal the dependence of the time interval [0,T0] in which the problem admits a solution. More precisely, T0 depends only on Lr|u0| and f. 相似文献
12.
13.
Shiping Lu 《Journal of Mathematical Analysis and Applications》2007,336(2):1107-1123
By means of Mawhin's continuation theorem, a kind of p-Laplacian differential equation with a deviating argument as follows:
(φp(x′(t)))′=f(t,x(t),x(t−τ(t)),x′(t))+e(t) 相似文献
14.
15.
利用重合度理论和一些分析技巧,得到一类二阶时滞Duffing微分方程的2kT周期解,通过对该微分方程的一系列周期解取极限获得同宿解的存在性.同时,β(t)是可变号的. 相似文献
16.
Sufficient criteria are established for the existence of periodic solutions to a type of Duffing equation with state-dependent delay, which improve and generalize some related results in the literature. The approach is based on Mawhin’s continuation theorem. The significance of the present paper is that our results are relevant to delay by Lemma 2.1, which is different from the corresponding results of past work. 相似文献
17.
《Nonlinear Analysis: Theory, Methods & Applications》2011,74(10):3232-3241
For higher-order nonautonomous linear and nonlinear differential equations with deviating arguments, new sufficient conditions of existence and uniqueness of a periodic solution are found. 相似文献
18.
In this article, we establish the existence and uniqueness results for solutions of a class of initial value problems of nonlinear fractional differential systems on half lines involving Riemann–Liouville fractional derivatives. Our analysis relies on the well-known fixed point theorem of Schauder. The novelty of this paper is that the problems discussed are defined on half lines, and the nonlinearities f and g are allowed to be singular functions. Furthermore, we allow p∈(0,β) and q∈(0,α). 相似文献
19.
In this paper, we study the existence of periodic solutions for a fourth-order p-Laplacian differential equation with a deviating argument as follows:
[φp(u″(t))]″+f(u″(t))+g(u(t−τ(t)))=e(t).