This paper is contributed to the study of the Cauchy problem <: ut = ∆u+K(|x|)up + μf(|x|) in Rn × (0, T ), u(x, 0) = φ(x) in Rn, u(x, 0) = φ(x) in Rn, with non-negative initial function φ 6≡ 0. We will study the asymptotic behavior and the semistability of the minimal positive steady state. In addition, we will prove that all slow decay positive steady states are stable and weakly asymptotical...

For a class of semi-linear elliptic equations with critical Sobolev exponents and boundary conditions, we prove point-wise estimates for blowup solutions and energy estimates. A special case of this class of equations is a locally defined prescribing scalar curvature and mean curvature type equation.

The inverse problem of identifying an unknown source control param- eter in a semilinear parabolic equation under an integral overdetermina- tion condition is considered. The series pattern solution of the proposed problem is obtained by using the weighted homotopy analysis method (WHAM). A description of the method for solving the problem and nding the unknown parameter is derived. Finally, tw...

A semilinear space S is a non-empty set of elements called points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every line contains at least two points. Two points p and q are said to be collinear if p 6ˆ q and if the pair f p; qg is contained in a line; the line containing two collinear points p and q will be denoted by pq...

Two nontrivial solutions are obtained for nonhomogeneous semilinear Schrödinger equations.

We consider the quantifier-free languages, Bc and Bc◦, obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected interior. These languages are interpreted over the regular closed sets of Rn (n ≥ 2) and, additionally, over the regular closed semilinear sets of Rn. The resulti...

Convergence of certain transforms of Markov processes generators implies large deviations. In this article, we apply abstract theorems of such type to stochastic evolution equations in real separable Hilbert space, giving diierent perspectives and extensions to some known results. When the drift term is semilinear, the rate function is explicitly identiied. The main large deviation theorem 18 3...

In this paper, we investigate residual-based a posteriori error estimates for the hp finite element approximation of semilinear Neumann boundary elliptic optimal control problems. By using the hp finite element approximation for both the state and the co-state and the hp discontinuous Galerkin finite element approximation for the control, we derive a posteriori error bounds in L2-H1 norms for t...

Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using...

Let Gk denote the set of all k-dimensional subspaces of an n-dimensional vector space. We recall that two elements of Gk are called adjacent if their intersection has dimension k − 1. The set Gk is point set of a partial linear space, namely a Grassmann space for 1 < k < n − 1 (see Section 5) and a projective space for k ∈ {1, n − 1}. Two adjacent subspaces are—in the language of partial linear...