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Full-Text Articles in Mathematics
Existence And Nonexistence Results For A Class Of Quasilinear Elliptic Systems, Said El Manouni
Existence And Nonexistence Results For A Class Of Quasilinear Elliptic Systems, Said El Manouni
Mathematics and System Engineering Faculty Publications
Using variational methods, we prove the existence and nonexistence of positive solutions for a class of -Laplacian systems with a parameter.
Constant-Sign Solutions Of A System Of Integral Equations With Integrable Singularities, Ravi P. Agarwal, Donal O'Regan, Patricia J.Y. Wong
Constant-Sign Solutions Of A System Of Integral Equations With Integrable Singularities, Ravi P. Agarwal, Donal O'Regan, Patricia J.Y. Wong
Mathematics and System Engineering Faculty Publications
We consider the following systems of Fredholm integral equations and the system of Volterra integral equations where the nonlinearities fi, 1 ≤ i ≤ n may be singular in the independent variable and may also be singular at uj = 0, j ∈ {1, 2,..., n}. Our aim is to establish criteria such that the above systems have at least one constant-sign solution (u1, u2,..., un), i.e., for each 1 ≤ i ≤ n, Θiui ≥ 0 where Θi ∈ {1,-1} is fixed. © 2007 Rocky Mountain Mathematics Consortium.
Preprocessing Of Sar Interferometric Data Using Anisotropic Diffusion Filter, Kenneth Sartor, Josef Vaughn De Allen, Emile Ganthier, Gnana Bhaskar Tenali
Preprocessing Of Sar Interferometric Data Using Anisotropic Diffusion Filter, Kenneth Sartor, Josef Vaughn De Allen, Emile Ganthier, Gnana Bhaskar Tenali
Mathematics and System Engineering Faculty Publications
The most commonly used smoothing algorithms for complex data processing are blurring functions (i.e., Hanning, Taylor weighting, Gaussian, etc.). Unfortunately, the filters so designed blur the edges in a Synthetic Aperture Radar (SAR) scene, reduce the accuracy of features, and blur the fringe lines in an interferogram. For the Digital Surface Map (DSM) extraction, the blurring of these fringe lines causes inaccuracies in the height of the unwrapped terrain surface. Our goal here is to perform spatially non-uniform smoothing to overcome the above mentioned disadvantages. This is achieved by using a Complex Anisotropic Non-Linear Diffuser (CANDI) filter that is a …
Anisotropic Diffusion Techniques On Synthetic Aperture Radar Data, Josef Vaughn De Allen, Emile Ganthier, Gnana Bhaskar Tenali
Anisotropic Diffusion Techniques On Synthetic Aperture Radar Data, Josef Vaughn De Allen, Emile Ganthier, Gnana Bhaskar Tenali
Mathematics and System Engineering Faculty Publications
Speckle in SAR imagery is a by-product of constructive and destructive interference between scatterers within a resolution cell. This speckle phenomenon gives SAR imagery a "noise-like" appearance and is often exploited in near angle and/or coherent stereo pairs. However, in many cases, this speckle is unwanted and can be considered noise or interference. We use partial differential equation (PDE) methods for speckle mitigation in detected imagery and the collected complex image data. In particular, we study the effects of non-linear anisotropic diffusion filters on collected SAR image data. In the past, anisotropic diffusion (AD) techniques have been successfully used in …
Existence To Singular Boundary Value Problems With Sign Changing Nonlinearities Using An Approximation Method Approach, Haishen Lu, Donal O'Regan, Ravi P. Agarwal
Existence To Singular Boundary Value Problems With Sign Changing Nonlinearities Using An Approximation Method Approach, Haishen Lu, Donal O'Regan, Ravi P. Agarwal
Mathematics and System Engineering Faculty Publications
This paper studies the existence of solutions to the singular boundary value problem {−u′′=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), {−u″=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), , where g: (0, 1) × (0, ∞) → ℝ and h: (0, 1) × [0, ∞) → [0, ∞) are continuous. So our nonlinearity may be singular at t = 0, 1 and u = 0 and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.
New Integral Inequalities For Iterated Integrals With Applications, Ravi P. Agarwal, Cheonseoung Ryoo
New Integral Inequalities For Iterated Integrals With Applications, Ravi P. Agarwal, Cheonseoung Ryoo
Mathematics and System Engineering Faculty Publications
Some new nonlinear retarded integral inequalities of Gronwall type are established. These inequalities can be used as basic tools in the study of certain classes of integrodifferential equations.
Reaction-Diffusion In Nonsmooth And Closed Domains, Ugur G. Abdulla
Reaction-Diffusion In Nonsmooth And Closed Domains, Ugur G. Abdulla
Mathematics and System Engineering Faculty Publications
We investigate the Dirichlet problem for the parabolic equation in a nonsmooth and closed domain possibly formed with irregular surfaces and having a characteristic vertex point. Existence, boundary regularity, uniqueness, and comparison results are established. The main objective of the paper is to express the criteria for the well-posedness in terms of the local modulus of lower semicontinuity of the boundary manifold. The two key problems in that context are the boundary regularity of the weak solution and the question whether any weak solution is at the same time a viscosity solution.
Philos-Type Oscillation Criteria For Second Order Half-Linear Dynamic Equations On Time Scales, Ravi P. Agarwal, Donal O'Regan, Samir H. Saker
Philos-Type Oscillation Criteria For Second Order Half-Linear Dynamic Equations On Time Scales, Ravi P. Agarwal, Donal O'Regan, Samir H. Saker
Mathematics and System Engineering Faculty Publications
In this paper we establish some oscillation theorems for the second order half-linear dynamic equation (r(t)(x Δ(t) γ) Δ + p(t)x γ(t) = 0, ∈ [a,b], on time scales. Special cases of our results include some well-known oscillation results for second-order differential and half-linear differential equations. Our results are new for difference, generalized difference and q difference half-linear equations. Copyright © 2007 Rocky Mountain Mathematics Consortium.