Titles and Short Summaries of the Talks

41 Functional Equations
Final: 2013/2/7
15 Haruya Mizutani (Gakushuin Univ.) ♯ Remarks on Strichartz estimates for Schrödinger equations with potentials
superquadratic at infinity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We study local-in-time Strichartz estimates with loss of derivatives for Schrödinger
equations with variable coefficients and electromagnetic potentials, under the conditions that the
geodesic flow is nontrapping and convex and that potentials grow supercritically at infinity.
16 Tetsutaro Shibata (Hiroshima Univ.) ∗ Inverse bifurcation problems for diffusive logistic equation of population
dynamics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We consider the nonlinear eigenvalue problem arising in population dynamics with
unknown nonlinear term f(u). Our focus is inverse bifurcation problem in L 1 -framework. Precisely,
we prove that the asymptotic behavior of L 1 -bifurcation curve λ(α) as α → ∞ determines f(u)
uniquely, where α := ∥uλ∥1.
17 Yutaka Kamimura
(Tokyo Univ. of Marine Sci. and Tech.)
♯ An inverse analysis of advection-diffusion · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We consider an ocean circulation inverse problem to determine unknown velocity
field and diffusivities of the time-independent advection-diffusion equation from data of a tracer.
A reconstruction formula is shown in terms of a solution to Marchenko-type integral equation.
Moreover a necessary and sufficient condition for an analytic function in the right half-plane to be
a tacer data is shown. A uniqueness result for the velocity field and diffusuvities is also shown
16:45–17:45 Talk invited by Functional Equations Section
Naoto Yamaoka (Osaka Pref. Univ.) ♯ An oscillation constant for half-linear differential equations and its
application
9:30–12:00
Summary: This talk is concerned with the oscillation problem for the half-linear differential
equations (a(t)|x ′ | p−2 x ′ ) ′ +b(t)|x| p−2 x = 0, where p > 1, and a(t), b(t) are positive and continuous on
(0, ∞). A typical example of the equation is the generalized Euler differential equation (|x ′ | p−2 x ′ ) ′ +
δ|x| p−2 x/t p = 0, where δ > 0. It is known that the condition δ > ((p − 1)/p) p is necessary and
sufficient for all nontrivial solutions of the generalized Euler differential equation to be oscillatory.
Some results for half-linear or more general nonlinear differential equations are obtained by the
condition. Moreover, elliptic equations with p-Laplacian operator are discussed as an application
to the results.
March 21st (Thu) Conference Room IV
18 Satoshi Tanaka (Okayama Univ. of Sci.) ♯ Exact multiplicity of positive solutions for a class of two-point boundary
value problems with one-dimensional p-Laplacian · · · · · · · · · · · · · · · · · · 15
Summary: Employing Kolodner–Coffman method, we show the exact multiplicity of positive
solutions for one-dimensional p-Laplacian which is subject to Dirichlet boundary condition with
a positive convex nonlinearity and an indefinite weight function. Moreover, the results obtained
here are applied to the study of radially symmetric solutions of the Dirichlet problem for elliptic
equations in annular domains.