scholarly journals Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian

2004 ◽  
Vol 298 (1) ◽  
pp. 245-260 ◽  
Author(s):  
Diego Averna ◽  
Roberta Salvati
Keyword(s):  
Boundary Value Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Value Problem ◽  
Three Solutions ◽  
One Dimensional ◽  
The One

scholarly journals On a Conjecture for the One-Dimensional Perturbed Gelfand Problem for the Combustion Theory

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2137
Author(s):  
Huizeng Qin ◽  
Youmin Lu
Keyword(s):  
Boundary Value Problem ◽  
Numerical Computation ◽  
Unique Solution ◽  
Boundary Value ◽  
Boundary Values ◽  
Three Solutions ◽  
One Dimensional ◽  
The One ◽  
Gelfand Problem ◽  
Existing Result

We investigate the well-known one-dimensional perturbed Gelfand boundary value problem and approximate the values of α0,λ* and λ* such that this problem has a unique solution when 0<α<α0 and λ>0, and has three solutions when α>α0 and λ*<λ<λ*. The solutions of this problem are always even functions due to its symmetric boundary values and autonomous characteristics. We use numerical computation to show that 4.0686722336<α0<4.0686722344. This result improves the existing result for α0≈4.069 and increases the accuracy of α0 to 10−8. We developed an algorithm that reduces errors and increases efficiency in our computation. The interval of λ for this problem to have three solutions for given values of α is also computed with accuracy up to 10−14.

scholarly journals Multiple positive solutions to mixed boundary value problems for singular ordinary differential equations on the whole line

2012 ◽  
Vol 17 (4) ◽  
pp. 460-480 ◽  
Author(s):  
Yuji Yuji
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Nonnegative Function ◽  
Multiple Positive Solutions ◽  
Mixed Boundary Value Problem ◽  
One Dimensional ◽  
Singular Ordinary Differential Equation ◽  
The One

This paper is concerned with the mixed boundary value problem of the second order singular ordinary differential equation[Φ(ρ(t)x'(t))]' + f(t, x(t), x'(t)) = 0,   t ∈ R,limt→−∞ x(t) = ∫−∞+∞ g(s, x(s), x'(s)) ds,limt→+∞ ρ(t)x'(t) =  ∫−∞+∞h(s, x(s), x' (s)) ds.Sufficient conditions to guarantee the existence of at least one positive solution are established. The emphasis is put on the one-dimensional p-Laplacian term [Φ(ρ(t)x'(t))]' involved with the nonnegative function ρ satisfying ∫−∞+∞1/ρ(s) ds = +∞.

scholarly journals Uniqueness and stability of solutions for a type of parabolic boundary value problem

1989 ◽  
Vol 12 (4) ◽  
pp. 735-739
Author(s):  
Enrique A. Gonzalez-Velasco
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Nonnegative Solution ◽  
Boundary Value ◽  
Stability Of Solutions ◽  
General Boundary Conditions ◽  
Boundary Values ◽  
Parabolic Boundary ◽  
One Dimensional ◽  
The One

We consider a boundary value problem consisting of the one-dimensional parabolic equationgut=(hux)x+q, where g, h and q are functions of x, subject to some general boundary conditions. By developing a maximum principle for the boundary value problem, rather than the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.

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