共查询到20条相似文献,搜索用时 15 毫秒
1.
Chang-Kwon Choi 《Indagationes Mathematicae》2019,30(1):240-249
Let be a real normed vector space and . In this paper, we prove the hyperstability of the logarithmic functional equation on of Lebesgue measure zero. More precisely, we prove that if satisfies for all of Lebesgue measure zero, where is an arbitrary given function and satisfies the condition as [resp. ], then satisfies the functional equation for all and. 相似文献
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This paper is concerned with the well-posedness and asymptotic behavior of Dirichlet initial boundary value problem for a singular parabolic p-biharmonic equation with logarithmic nonlinearity. We establish the local solvability by the technique of cut-off combining with the methods of Faedo–Galerkin approximation and multiplier. Meantime, by virtue of the family of potential wells, we use the technique of modified differential inequality and improved logarithmic Sobolev inequality to obtain the global solvability, infinite and finite time blow-up phenomena, and derive the upper bound of blow-up time as well as the estimate of blow-up rate. Furthermore, the results of blow-up with arbitrary initial energy and extinction phenomena are presented. 相似文献
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一个Gauss型函数方程 总被引:3,自引:0,他引:3
刘证 《纯粹数学与应用数学》2002,18(1):53-57,62
给出了任意两个正实数的几何-调和平均值的一个积分表示式,并由此去探讨了函数方程f(ab,2ab/a+b)=f(a,b),a,b>0其中f:R+×R+→R是此方程的一个未知函数. 相似文献
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In this paper, the backward problem for space-fractional diffusion equation is investigated. We proposed a so-called logarithmic regularization method to solve it. Based on the conditional stability and an a posteriori regularization parameter choice rule, the convergence rate estimates are given under a-priori bound assumption for the exact solution. 相似文献
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Vichian Laohakosol Watcharapon Pimsert 《Journal of Mathematical Analysis and Applications》2011,375(2):777-789
The functional equation af(xy)+bf(x)f(y)+cf(x+y)+d(f(x)+f(y))=0 whose shape contains all the four well-known forms of Cauchy's functional equation is solved for solutions which are functions having the positive reals as their domain. This complements an earlier work of Dhombres in 1988 where the same functional equation was solved for solutions whose domains contain zero, which leaves out the logarithmic function. Here not only the logarithmic function is recovered but the analysis is entirely different and is based on solving appropriate difference equations. 相似文献
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Young Whan Lee Byung Mun Choi 《Journal of Mathematical Analysis and Applications》2004,299(2):305-313
We obtain the super stability of Cauchy's gamma-beta functional equation
B(x,y)f(x+y)=f(x)f(y), 相似文献
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In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation
2f(x + 2y) + f(2x - y) = 5f(x + y) + 5f(x - y)+ 15f(y)
in the spirit of Hyers, Ulam, Rassias and Gavruta. 相似文献
2f(x + 2y) + f(2x - y) = 5f(x + y) + 5f(x - y)+ 15f(y)
in the spirit of Hyers, Ulam, Rassias and Gavruta. 相似文献
11.
Abbas Najati 《Journal of Mathematical Analysis and Applications》2008,340(1):569-574
In this paper, we prove the generalized Hyers-Ulam stability for the following quartic functional equation
f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y). 相似文献
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Another logarithmic functional equation 总被引:1,自引:0,他引:1
K. J. Heuvers 《Aequationes Mathematicae》1999,58(3):260-264
Summary. Let f : ]0,¥[? \Bbb R f :\,]0,\infty[\to \Bbb R be a real valued function on the set of positive reals. The functional equations¶¶f(x + y) - f(x) - f(y) = f(x-1 + y-1) f(x + y) - f(x) - f(y) = f(x^{-1} + y^{-1}) ¶and¶f(xy) = f(x) + f(y) f(xy) = f(x) + f(y) ¶are equivalent to each other. 相似文献
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Jae-Hyeong Bae 《Journal of Mathematical Analysis and Applications》2007,326(2):1142-1148
In this paper, we obtain the general solution and the stability of the 2-variable quadratic functional equation
f(x+y,z+w)+f(x−y,z−w)=2f(x,z)+2f(y,w). 相似文献
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We study the initial boundary value problem of a semilinear heat equation with logarithmic nonlinearity. By using the logarithmic Sobolev inequality and a family of potential wells, we obtain the existence of global solution and blow-up at +∞ under some suitable conditions. On the other hand, the results for decay estimates of the global solutions are also given. Our result in this paper means that the polynomial nonlinearity is a critical condition of blow-up in finite time for the solutions of semilinear heat equations. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(4):1541-1553
In this paper we solve an initial‐boundary value problem that involves a pde with a nonlocal term. The problem comes from a cell division model where the growth is assumed to be stochastic. The deterministic version of this problem yields a first‐order pde; the stochastic version yields a second‐order parabolic pde. There are no general methods for solving such problems even for the simplest cases owing to the nonlocal term. Although a solution method was devised for the simplest version of the first‐order case, the analysis does not readily extend to the second‐order case. We develop a method for solving the second‐order case and obtain the exact solution in a form that allows us to study the long time asymptotic behaviour of solutions and the impact of the dispersion term. We establish the existence of a large time attracting solution towards which solutions converge exponentially in time. The dispersion term does not appear in the exponential rate of convergence. 相似文献
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In this article, we establish the stability of the orthogonally cubic type functional equation (1.2) for all x1,x2,x3 with xi⊥xj(i,j=1,2,3), where ⊥ is the orthogonality in the sense of Rätz, and investigate the stability of the n-dimensional cubic type functional equation (1.3), where n?3 is an integer. 相似文献
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In this paper, we study the existence of ground state solutions of nonlinear elliptic equation with logarithmic nonlinearity by the Linking theorem and logarithmic Sobolev inequality. Our results are quite different from those in the case of polynomial nonlinearity. 相似文献
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《Stochastic Processes and their Applications》2020,130(9):5838-5864
We consider the two-dimensional stochastic damped nonlinear wave equation (SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In particular, we investigate the limiting behavior of solutions to SdNLW with regularized noises and establish triviality results in the spirit of the work by Hairer et al. (2012). More precisely, without renormalization of the nonlinearity, we establish the following two limiting behaviors; (i) in the strong noise regime, we show that solutions to SdNLW with regularized noises tend to 0 as the regularization is removed and (ii) in the weak noise regime, we show that solutions to SdNLW with regularized noises converge to a solution to a deterministic damped nonlinear wave equation with an additional mass term. 相似文献