Quasilinear fractional differential equation with resonance boundary condition

In this paper, we consider quasilinear fractional differential equation with resonance boundary condition. After translating the quasilinear equation into the linear fractional differential system, by using coincidence degree theory, the existence result is established

The existence of solutions for -Laplacian boundary value problems at resonance on the half-line

The concept of collective efficacy, defined as the combination of mutual trust and willingness to act for the common good, has received widespread attention in the field of criminology. Collective efficacy is linked to, among other outcomes, violent crime, disorder, and fear of crime. The concept has been applied to geographical units ranging from below one hundred up to several thousand residents on average. In this paper key informant- and focus group interview transcripts from four Swedish neighborhoods are examined to explore whether different sizes of geographical units of analysis are equally important for collective efficacy. The four studied neighborhoods are divided into micro-neighborhoods (N=12) and micro-places (N=59) for analysis. The results show that neighborhoods appear to be too large to capture the social mechanism of collective efficacy which rather takes place at smaller units of geography. The findings are compared to survey responses on collective efficacy (N=597) which yield an indication in the same direction through comparison of ICC-values and AIC model fit employing unconditional two-level models in HLM 6

Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations

We consider three problems for the Helmholtz equation in interior and exterior domains in R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for exterior Helmholtz problems.Comment: Version 3: 42 pages; improved exposition in response to referee comments and added several reference

Current Density Impedance Imaging of an Anisotropic Conductivity in a Known Conformal Class

We present a procedure for recovering the conformal factor of an anisotropic conductivity matrix in a known conformal class in a domain in Euclidean space of dimension greater than or equal to 2. The method requires one internal measurement, together with a priori knowledge of the conformal class (local orientation) of the conductivity matrix. This problem arises in the coupled-physics medical imaging modality of Current Density Impedance Imaging (CDII) and the assumptions on the data are suitable for measurements determinable from cross-property based couplings of the two imaging modalities CDII and Diffusion Tensor Imaging (DTI). We show that the corresponding electric potential is the unique solution of a constrained minimization problem with respect to a weighted total variation functional defined in terms of the physical data. Further, we show that the associated equipotential surfaces are area minimizing with respect to a Riemannian metric obtained from the data. The results are also extended to allow the presence of perfectly conducting and/or insulating inclusions

On a Resonant Fractional Order Multipoint and Riemann-Stieltjes Integral Boundary Value Problems on the Half-line with Two-dimensional Kernel

This paper investigates existence of solutions of a resonant fractional order boundary value problem with multipoint and Riemann-Stieltjes integral boundary conditions on the half-line with two-dimensional kernel. We utilised Mawhin’s coincidence degree theory to derive our results. The results obtained are validated with examples

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder’s fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables