Exact theoretical results are
obtained for critical state of thin superconductors with field-dependent
critical current, Jc.
We have determined that the low-field peak in major magnetization
loops of thin strips 
is found at zero applied field for any Jc(B)-dependence.
We calculated flux and
current distributions as well as magnetization and ac susceptibility for a thin disk
with a general Jc(B)-dependence.
Spatial inhomogeneity of HTSC films
Due to anomalously small coherence length and a very complicated crystal
structure properties of HTSC are strongly affected by various spatial inhomogeneities.
We have studied effect of Tc-inhomogeneity on resistance
[1,2] and its noise
in the vicinity of superconducting transition; methods to measure Tc-inhomogeneity
by low-temperature SEM [1,4];
correlation between Tc- and jc-inhomogeneity
[5,6] observed by magneto-optical
imaging and relation of spatial inhomogeneities to cation defect formation
Magnetic flux penetration
into HTSC films
Penetration of magnetic flux
into HTSC samples of various shapes can now be easily visualized by magneto-optical
and other spatially-resolved techniques. We studied flux penetration into
a thin current-carrying strip and compared experimental results with the
Bean model predictions and our flux creep simulations .
Besides, we observed an evolution of flux distribution after switching
on transport current .
Using magneto-optical imaging
a temperature dependence of filament coupling in Bi-2223 tapes have been
We also studied a large- and small-scale structure of flux distrbution in various
current-carrying states of Bi-2223 tapes
Resistance flicker noise
Studies of flicker noise are of great interest because, first, this noise
limits sensitivity of HTSC devices, and, second, such studies present a
powerful tool to characterize a degree of structural disorder. We have
studied resistance flicker noise in the normal phase 
and in the vicinity of Tc 
as well as noise of a single latent weak link below the transition .
Theoretical models for noise associated with local fluctuations of Tc
 as well as with temperature fluctuations 
have been considered.
Novel HF devices
Some ideas are suggested for fabrication of new and advancement of existing
HF devices based on HTSC. A parametric resonance due to temperature oscillations
in superconducting micron-scale waveguides under laser beam irradiation
is suggested for the creation of high-sensitivity tuneable filters .
Use of the resonance effect in bolometers based on superconductors in the
zero-resistance state is suggested to reach the signal/noise ratio above
that of conventional bolometers .