Keywords: Dirichlet boundary value problem p-Laplacian Topological degree theory Critical point theory Weak solution a b s t r a c t In this work, by virtue of topological degree theory and critical point theory, we are mainly concerned with the existence of weak solutions for a Dirichlet boundary value problem with the p-Laplacian operator.

In this paper, we consider the long time behavior of solutions for two-dimensional generalized Benjamin-Bona-Mahony equations with periodic boundary conditions. By the method of orthogonal decomposition, we show that the existence of asymptotic attractor from the precision of approximate inertial manifolds. Moreover, the dimensions estimate of the asymptotic attractor is obtained.

Methods We obtained OCT images of normal, benign, premalignant and malignant lesions in different areas of the head and neck. The OCT imaging system has a tissue penetration depth of approximately 1-2mm, a scanning range of 2mm and a spatial depth resolution of approximately 10-20μm. Imaging was performed using a flexible probe in two different situations, the outpatient clinic and the operatin...

We present a new method to simulate repetitive ferromagnetic structures. This macro geometry approach combines treatment of short-range interactions (i.e. the exchange field) as for periodic boundary conditions with a specification of the arrangement of copies of the primary simulation cell in order to correctly include effects of the demagnetizing field. This method (i) solves a consistency pr...

A new theorem is applied to the Kuramoto-Sivashinsky equation with L-periodic boundary conditions, proving the existence of an asymptotically complete inertial manifold attracting all initial data. Combining this result with a new estimate of the size of the globally absorbing set yields an improved estimate of the dimension, N ∼ L.

We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f :R→ R is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant β > 0 such that u f (u) > 0 whenever |u| ≥ β. For such an equation we prove that ifN is an odd integer...

We study a linear fractional differential equation with a periodic boundary condition and give the explicit form of the solution and the corresponding Green’s function. Using some properties of the Green’s function we present some new comparison results.

The nonlinear eigenvalue problem of the differential equation ( |x′|p−2 x′ )′ + (λ+ c(t)) |x|p−2 x = 0, p > 1, with respect to the periodic boundary conditions: x(0) = x(T ), x′(0) = x′(T ), or to the antiperiodic boundary conditions: x(0) = −x(T ), x′(0) = −x′(T ) are considered. Various results on the set of eigenvalues concerning both problems are presented. Some estimates are given for the ...

We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of Þxed or free boundary curves in R, S and H. The algorithm makes no restriction on the genus and can handle singular triangulations. For a discrete harmonic map a conjugation process is presented leading in case of minimal surfaces additionally to instable solutions of the free boundary value problem fo...

Depression severely affects older adults in the United States. As part of the social environment, significant social support was suggested to ameliorate depression among older adults. We investigate how varying forms of social support moderate depressive symptomatology among older adults with multiple chronic conditions (MCC). Data were analyzed using a sample of 11,400 adults, aged 65 years or...