Funkcialaj Ekvacioj

Ground States and Singular Ground States for Quasilinear Elliptic Equation in the Subcritical Case

Matteo Franca

2005 年 48 巻 3 号 p. 331-349
発行日: 2005年
公開日: 2005/12/22

DOIhttps://doi.org/10.1619/fesi.48.331

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We consider radial solution u(|x|), x ∈ Rⁿ, of a p-Laplace equation with non-linear potential depending also on the space variable x. We assume that the potential is polynomial and it is negative for u small and positive and subcritical for u large.
We prove the existence of radial Ground States under suitable Hypotheses on the potential f(u,|x|). Furthermore we prove the existence of uncountably many radial Singular Ground States; this last result seems to be new even for the spatial independent case and even for p=2.
The proofs combine an energy analysis and the dynamical systems approach developed by Johnson, Pan, Yi and Battelli for the p=2 case.

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Local Energy Decay for Linear Wave Equations with Localized Dissipation

Ryo Ikehata

2005 年 48 巻 3 号 p. 351-366
発行日: 2005年
公開日: 2005/12/22

DOIhttps://doi.org/10.1619/fesi.48.351

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A local energy decay result can be derived for a linear wave equation in an exterior domain Ω ⊂ R^N, which has a localized dissipation being effective only near a part of the boundary ∂Ω. In this case we do not assume any compactness of the support on the initial data differently from the usual well-known case. Our result generalizes some previous results due to Morawetz [9], Nakao [12], Ikehata [4] and Ikehata-Nishihara [6].

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Stability Properties of Linear Volterra Integrodifferential Equations in a Banach Space

Yoshiyuki Hino, Satoru Murakami

2005 年 48 巻 3 号 p. 367-392
発行日: 2005年
公開日: 2005/12/22

DOIhttps://doi.org/10.1619/fesi.48.367

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For linear Volterra integrodifferential equations, we characterize the uniform asymptotic stability property of the zero solution by a property for the resolvent operator. In particular, for equations of convolution type, we characterize the uniform asymptotic stability property in terms of the integrability of the resolvent operator, as well as the invertibility of the characteristic operator. Furthermore, we apply our results to nonhomogeneous equations with asymptotically almost periodic forcing terms, and establish some results on the existence of asymptotically almost periodic solutions.

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More on the Behavior of Solutions to Linear Integrodifferential Equations with Unbounded Delay

Ch. G. Philos, I. K. Purnaras

2005 年 48 巻 3 号 p. 393-414
発行日: 2005年
公開日: 2005/12/22

DOIhttps://doi.org/10.1619/fesi.48.393

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Linear neutral, and especially non-neutral, integrodifferential equations with unbounded delay are considered. Via two appropriate distinct real roots of the corresponding characteristic equations, some new results on the behavior of solutions are obtained.

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A Model for the Jeans Instability in One-Dimensional Motion of Compressible Viscous Gases

Yoritaka Iwata, Yoshitaka Yamamoto

2005 年 48 巻 3 号 p. 415-451
発行日: 2005年
公開日: 2005/12/22

DOIhttps://doi.org/10.1619/fesi.48.415

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The Jeans instability is an astrophysical idea associated with the collapse of a fluctuated infinite homogeneous self-gravitating gas. If a fluctuation ideally takes the form of a plane wave, then the growth of the wavelength is a factor of the instability. As a model we consider a system of equations describing the one-dimensional periodic motion of a self-gravitating viscous gas. Concerning the model system we study the structure of the whole stationary solutions, the asymptotic behavior of solutions, and the nonlinear stability of stationary solutions. The Jeans instability is closely related with bifurcation of solutions in the stationary problem of the model system.

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Local Solvability of Operators with Principal Symbol ξ²₁+…+ξ²_n−1+x²_nξ²_n in the Spaces of Distributions and Ultradistributions

Seiichiro Wakabayashi

2005 年 48 巻 3 号 p. 453-487
発行日: 2005年
公開日: 2005/12/22

DOIhttps://doi.org/10.1619/fesi.48.453

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In this paper we shall illustrate how to study local solvability in the spaces of distributions and ultradistributions through the studies on operators of a special form. We shall give necessary conditions and sufficient conditions for these operators.

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