A High-Temperature Superconducting Bandpass Dual-Mode Filter with Tunable Relative Bandwidth and Center Frequency.

This study proposes a high-temperature superconducting (HTS) bandpass filter with a continuously tunable bandwidth and center frequency. The proposed filter combines several gallium arsenide varactors and a dual-mode resonator (DMR). The even and odd modes of the DMR can be tuned simultaneously using a single bias voltage. The capacitive value of varactors in the circuit is tuned continuously under continuous voltage and frequency tunability. External couplings and the interstage can be realized using an interdigital coupling structure; a fixed capacitor is added to the feeder to improve its coupling strength. A low-insertion loss within the band is obtained using HTS technology. Additionally, the proposed filter is etched on a 0.5 mm-thick MgO substrate and combined with YBCO thin films for demonstration. For the as-fabricated device, the tuning frequency range of 1.22~1.34 GHz was 9.4%; the 3-dB fractional bandwidth was 12.95~17.39%, and the insertion loss was 2.28~3.59 dB. The simulation and experimental measurement results were highly consistent.

Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian.

The present study is concerned with the following fractional p-Laplacian equation involving a critical Sobolev exponent of Kirchhoff type: [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants, and [Formula: see text] is the fractional p-Laplacian operator with [Formula: see text] and [Formula: see text]. For suitable [Formula: see text], the above equation possesses at least two nontrivial solutions by variational method for any [Formula: see text]. Moreover, we regard [Formula: see text] and [Formula: see text] as parameters to obtain convergent properties of solutions for the given problem as [Formula: see text] and [Formula: see text], respectively.

Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy-Sobolev exponent and singular nonlinearity.

In this paper, we study a class of critical elliptic problems of Kirchhoff type: [ a + b ( ∫ R 3 | ∇ u | 2 - µ u 2 | x | 2 d x ) 2 - α 2 ] ( - Δ u - µ u | x | 2 ) = | u | 2 ∗ ( α ) - 2 u | x | α + λ f ( x ) | u | q - 2 u | x | ß , where a , b > 0 , µ ∈ [ 0 , 1 / 4 ) , α , ß ∈ [ 0 , 2 ) , and q ∈ ( 1 , 2 ) are constants and 2 ∗ ( α ) = 6 - 2 α is the Hardy-Sobolev exponent in R 3 . For a suitable function f ( x ) , we establish the existence of multiple solutions by using the Nehari manifold and fibering maps. Moreover, we regard b > 0 as a parameter to obtain the convergence property of solutions for the given problem as b ↘ 0 + by the mountain pass theorem and Ekeland's variational principle.