scholarly journals On the lifespan of classical solutions to a non-local porous medium problem with nonlinear boundary conditions

2020 ◽  
Vol 13 (7) ◽  
pp. 2033-2045
Author(s):  
Monica Marras ◽  
◽  
Nicola Pintus ◽  
Giuseppe Viglialoro
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Classical Solutions ◽  
Non Local

On Nonlinear Boundary Conditions Involving Decomposable Linear Functionals

2014 ◽  
Vol 58 (2) ◽  
pp. 421-439 ◽  
Author(s):  
Christopher S. Goodrich
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Linear Functional ◽  
Nonlinear Boundary ◽  
Nonlinear Function ◽  
Nonlinear Boundary Conditions ◽  
Stieltjes Integral ◽  
Linear Functionals ◽  
Non Local

AbstractIn this paper we consider the existence of a positive solution to boundary-value problems with non-local nonlinear boundary conditions, the archetypical example being −y″(t) = λf(t,y(t)),t∈ (0, 1),y(0) =H(φ(y)),y(1) = 0. Here,His a nonlinear function,λ> 0 is a parameter andφis a linear functional that is realized as a Lebesgue—Stieltjes integral with signed measure. By requiringφto decompose in a certain way, we show that this problem has at least one positive solution for eachλ∈ (0,λ0), for a numberλ0> 0 that is explicitly computable. We also give a separate result that holds for allλ> 0.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

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