On the Holomorphic Extension of Solutions of Elliptic Pseudodifferential Equations

2010 Mathematics Subject Classification: 35B65, 35S05, 35A20.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

Existence Theorems for Non-Cooperative Elliptic Systems

2010 Mathematics Subject Classification: 35J65, 35K60, 35B05, 35R05.

On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.