Fixed point theory for permissible extension type maps

Several new fixed point results for permissible self extension type maps are presented in this paper.     

Dead cores of singular Dirichlet boundary value problems with ϕ-Laplacian

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem (ϕ(u′))′ = λf(t, u, u′), u(0) = u(T) = A. Here λ is the positive parameter, A > 0, f is singular at the value 0 of its first phase variable and may be singular at the value A of its first and at the value 0 of its second phase variable. This work was supported by grant no. A100190703 of the Grant Agency of the Academy of Sciences of the Czech Republic and by the Council of Czech Government MSM 6198959214.     

Selective adaptation to frequency-modulated tones: evidence for an information-processing channel selectively sensitive to frequency changes.

Exposure to an FM tone elevates FM threshold but not AM threshold. This holds for a wide range of frequency deviations (delta F = +/- 0.4 Hz- +/- 30 Hz at least) provided that modulation frequency is low (fm = 2 Hz), but if fm is somewhat higher (e.g., 8 Hz) the finding only holds for small frequency deviations. FM threshold can rise with time up to an adapting duration of at least 1200 s, through this buildup depends on frequency deviation. Exposure to an AM tone elevates AM threshold, but not FM threshold, over a wide range of modulation depths (at least m = 5%--50%). Quasi-FM (QFM) adapting tones resemble FM adapting tones in their effects upon FM and AM sensitivities, even though QFM and AM adapting tones have identical power spectra. Exposure to a pure tone produces no difference between FM and AM threshold elevations. These data can be explained if the human auditory pathway contains separate information-processing channels for AM and FM signals whose sensitivities do not overlap even with suprathreshold stimuli. We suppose that the FM channel (but not the AM channel) is sensitive to changing differences (or ratios) between signals from different sites along the basilar membrane.     

On nonlinear integral equations and Λ-bounded variation

Summary We discuss the existence or the existence and uniqueness of global and local -bounded variation (BV) solutions as well as continuous BV-solutions of nonlinear Hammerstein and Volterra-Hammerstein integral equations formulated in terms of the Lebesgue integral. Since the space of functions of bounded variation in the sense of Jordan is a proper subspace of functions of -bounded variation and for some class of functions , the space of functions of bounded -variation in the sense of Young is also a proper subspace of the space under consideration, our results extend known results in the literature.     

Experimental evidence of guided-resonances in photonic crystals with aperiodically ordered supercells

We report on the first experimental evidence of guided resonances (GRs) in photonic crystal slabs based on aperiodically ordered supercells. Using Ammann-Beenker (quasiperiodic, eightfold symmetric) tiling geometry, we present our study on the fabrication, experimental characterization, and full-wave numerical simulation of two representative structures (with different filling parameters) operating at near-IR wavelengths (1300-1600 nm). Our results show a fairly good agreement between measurements and numerical predictions and pave the way for the development of new strategies (based on, e.g., the lattice symmetry breaking) for GR engineering.     

Controllability for noninstantaneous impulsive semilinear functional differential inclusions without compactness

The first part of this paper considers the controllability for a functional semilinear differential inclusion governed by a family of operators $\{A\left(t\right):t\in [0,b]\}$ generating an evolution operator in a Banach space in the presence of noninstantaneous impulse effects. In the second part of this paper we study the controllability for a fractional noninstantaneous impulsive semilinear differential inclusion with delay, where the linear part is an infinitesimal generator of a $C_0?$semigroup. Using a weakly convergent criterion in the space of piecewise continuous functions and weak topology theory (for weak sequentially closed graph operators) we establish sufficient conditions to guarantee controllability results. Examples are given to illustrate the abstract results.     

On second order differential equations with state-dependent delay

We study existence and uniqueness of solutions for a general class of second order abstract differential equations with state-dependent delay. Some examples related to partial differential equations with state dependent delay are presented.