Existence and uniqueness of the p-generalized modified error function
Copyright policy )Existence and uniqueness of the p-generalized modified error function
In this article, we define a p-generalized modified error function as the solution to a non-linear ordinary differential equation of second order, with a Robin type boundary condition at x=0. We prove existence and uniqueness of a non-negative \(C^{\infty}\) solution by using a fixed point argument. We show that the p-generalized modified error function converges to the p-modified error function defined as the solution to a similar problem with a Dirichlet boundary condition. In both problems, for p=1, the generalized modified error function and the modified error function are recovered. In addition, we analyze the existence and uniqueness of solution to a problem with a Neumann boundary condition. For more information see https://ejde.math.txstate.edu/Volumes/2020/35/abstr.html
- National Scientific and Technical Research Council Argentina
- CONICET Argentina
- Austral University Argentina
stefan problem, GENERALIZED MODIFIED ERROR FUNCTION, Nonlinear boundary value problems for ordinary differential equations, NONLINEAR ORDINARY DIFFERENTIAL EQUATION, Economics, Evolutionary biology, Positive solutions to nonlinear boundary value problems for ordinary differential equations, modified error function, banach fixed point theorem, Differential equation, Numerical Methods for Singularly Perturbed Problems, Classical Analysis and ODEs (math.CA), https://purl.org/becyt/ford/1.1, Boundary value problem, Numerical Analysis, Neumann boundary condition, Dirichlet boundary condition, Applied Mathematics, generalized modified error function, Nonlocal Partial Differential Equations and Boundary Value Problems, Algorithm, Mathematics - Classical Analysis and ODEs, Function (biology), Physical Sciences, STEFAN PROBLEM, nonlinear ordinary differential equation, Error Analysis, Other functions coming from differential, difference and integral equations, Uniqueness, Banach fixed point theorem, Mathematical analysis, Error function, Fixed-point theorems, Numerical Integration Methods for Differential Equations, QA1-939, FOS: Mathematics, MODIFIED ERROR FUNCTION, https://purl.org/becyt/ford/1, Biology, Order (exchange), Stefan problem, Applied mathematics, Boundary (topology), BANACH FIXED POINT THEOREM, Mathematics, Ordinary differential equation, Finance
stefan problem, GENERALIZED MODIFIED ERROR FUNCTION, Nonlinear boundary value problems for ordinary differential equations, NONLINEAR ORDINARY DIFFERENTIAL EQUATION, Economics, Evolutionary biology, Positive solutions to nonlinear boundary value problems for ordinary differential equations, modified error function, banach fixed point theorem, Differential equation, Numerical Methods for Singularly Perturbed Problems, Classical Analysis and ODEs (math.CA), https://purl.org/becyt/ford/1.1, Boundary value problem, Numerical Analysis, Neumann boundary condition, Dirichlet boundary condition, Applied Mathematics, generalized modified error function, Nonlocal Partial Differential Equations and Boundary Value Problems, Algorithm, Mathematics - Classical Analysis and ODEs, Function (biology), Physical Sciences, STEFAN PROBLEM, nonlinear ordinary differential equation, Error Analysis, Other functions coming from differential, difference and integral equations, Uniqueness, Banach fixed point theorem, Mathematical analysis, Error function, Fixed-point theorems, Numerical Integration Methods for Differential Equations, QA1-939, FOS: Mathematics, MODIFIED ERROR FUNCTION, https://purl.org/becyt/ford/1, Biology, Order (exchange), Stefan problem, Applied mathematics, Boundary (topology), BANACH FIXED POINT THEOREM, Mathematics, Ordinary differential equation, Finance
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