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Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn

Bachar Imed, Mâagli Habib, Eltayeb Hassan

Opuscula Mathematica

2022

Vol. 42, no. 6

793--803

In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of Rn (n ≥ 2). The global behavior of this solution is also given.

A Sign Function Approach to Solve Algebraically Interval System of Linear Equations for Nonnegative Solutions

Chakraverty S., Hladík M., Mahato N. R.

Fundamenta Informaticae

2017

Vol. 152, nr 1

13--31

This paper deals with solving interval system of linear equations. The problem is to find a nonnegative algebraic solution. Based on sign function approach and using interval center and radius arithmetic operations, we propose an algorithm for computation of an algebraic interval solution vector. We also discuss fundamental properties of this solution vector, such as existence and uniqueness. Further, the nonnegative solution algorithm has been extended to other signrestricted approach. Numerical examples of interval system of linear equations show efficiency of the algorithms presented.