共查询到20条相似文献,搜索用时 15 毫秒
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We study second and fourth order semilinear elliptic equations with a power-type nonlinearity depending on a power p and a parameter λ>0. For both equations we consider Dirichlet boundary conditions in the unit ball B⊂Rn. Regularity of solutions strictly depends on the power p and the parameter λ. We are particularly interested in the radial solutions of these two problems and many of our proofs are based on an ordinary differential equation approach. 相似文献
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《Stochastic Processes and their Applications》2020,130(1):366-393
In this paper, we consider stationarity of a class of second-order stochastic evolution equations with memory, driven by Wiener processes or Lévy jump processes, in Hilbert spaces. The strategy is to formulate by reduction some first-order systems in connection with the stochastic equations under investigation. We develop asymptotic behavior of dissipative second-order equations and then apply them to time delay systems through Gearhart–Prüss–Greiner’s theorem. The stationary distribution of the system under consideration is the projection on the first coordinate of the corresponding stationary results of a lift-up stochastic system without delay on some product Hilbert space. Last, two examples of stochastic damped wave equations with memory are presented to illustrate our theory. 相似文献
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Fabio Paronetto 《Journal of Differential Equations》2006,226(2):525-540
We give an existence and uniqueness result for a linear abstract evolution equation of second order with some coefficient in front of the second temporal derivative which may degenerate to zero and change sign. 相似文献
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We deal with the existence of periodic solutions for problems with a jump discontinuity. We use an approximation procedure and the method of the lower and upper solutions. 相似文献
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Mustafa Hasanbulli 《Applied mathematics and computation》2010,215(12):4392-4399
By refining the standard integral averaging technique, we obtain new oscillation criteria for a class of second order nonlinear neutral differential equations of the form
(r(t)(x(t)+p(t)x(t-τ))′)′+q(t)f(x(t),x(σ(t)))=0. 相似文献
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In this paper, the Banach fixed-point theorem is employed to establish several existence results of uncountably many bounded nonoscillatory solutions for the second order nonlinear neutral delay difference equation
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In this paper, we study the existence of positive periodic solutions for singular second order equations x" + n2/4x+h(x) = p(t), where h has a singularity at the origin and n is a positive integer. We give an explicit condition to ensure the existence of positive periodic solutions when h is an unbounded perturbation at infinity by using qualitative analysis and topological degree theory. 相似文献
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Hassan A. El-Morshedy S.R. Grace 《Journal of Mathematical Analysis and Applications》2005,306(1):106-121
New oscillation results are obtained for the second order nonlinear difference equation
Δ(rnf(Δxn−1))+g(n,xn)=0, 相似文献
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James S. W. Wong 《Proceedings of the American Mathematical Society》1999,127(5):1387-1395
We prove nonoscillation theorems for the second order Emden-Fowler equation (E): , , where and . It is shown that when is nondecreasing for any and is bounded above, then (E) is nonoscillatory. This improves a well-known result of Belohorec in the sublinear case, i.e. when and .
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Linghai Zhang 《Journal of Mathematical Analysis and Applications》2011,379(1):91-124
First of all, by using Bernoulli equations, we develop some technical lemmas. Then, we establish the explicit traveling wave solutions of five kinds of nonlinear evolution equations: nonlinear convection diffusion equations (including Burgers equations), nonlinear dispersive wave equations (including Korteweg-de Vries equations), nonlinear dissipative dispersive wave equations (including Ginzburg-Landau equation, Korteweg-de Vries-Burgers equation and Benjamin-Bona-Mahony-Burgers equation), nonlinear hyperbolic equations (including Sine-Gordon equation) and nonlinear reaction diffusion equations (including Belousov-Zhabotinskii system of reaction diffusion equations). 相似文献
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Yong-Hoon Lee 《Journal of Mathematical Analysis and Applications》2007,331(1):159-176
This paper studies the existence of extremal solutions for a class of singular boundary value problems of second order impulsive differential equations. By using the method of upper and lower solutions and the monotone iterative technique, criteria of the existence of extremal solutions are established. 相似文献
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Let H, V be two real Hilbert spaces such that VH with continuous and dense imbedding, and let FC1(V) be convex. By using differential inequalities, a close-to-optimal ultimate bound of the energy is obtained for solutions in to u″+cu′+bu+F(u)=f(t) whenever . 相似文献
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中立型二阶非线性微分方程振动性的判据 总被引:7,自引:0,他引:7
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