Existence d'orbites homoclines à un équilibre elliptique,pour un système réversible

We consider a reversible vector field in ℝ⁴, where the origin is a critical point, and where the differential at the origin has a pair of double non semisimple pure imaginary eigenvalues ±iw. We assume that the coefficient ε of a cubic term of the normal form is positive and close to 0, and that a certain coefficient of order 5 is negative. Then we show that there exist two reversible orbits homoclinic to the origin, of size √ε and such that they oscillate with a damping in 1/t when t tends towards ±∞. For obtaining such a result, we give explicitly the inverse of the linearized operator around the reversible homoclinics of the normal form, and solve the problem by a fixed point argument.     

Photoresponse of a miniaturized metal film bolometer to ultrashort mid- and far-infrared laser pulses

We report on an investigation of a photoresponse induced in a novel, miniaturized low-noise metal resistor film bolometer when irradiated by ultrashort laser pulses (duration 100 ps to 200 ns) with wavelengths covering the mid- and far-infrared spectral ranges. Successful operation at room temperature was achieved and almost constant detectivity was found over the whole frequency range investigated (15–1100 cm⁻¹). The minimum detectable laser pulse energy was determined to be about 0.6 μ J (with an electronic bandwidth of 1 kHz). This high detectivity and the miniaturized dimensions afford the possibility of building detector arrays applicable in mid- and far-infrared spectroscopy.     

p-Laplace非线性两点边值问题多个正解的存在性

本文利用一种新的三个泛函不动点定理得到了p-Laplacian方程在具有非线性边值条件时至少存在三个正解的充分条件,并且举了一个简单例子来说明得到的结论．