scholarly journals Positive Solution of Multi-Point Boundary Value Problem for the One-Dimensional $P$-Laplacian with Singularities

2007 ◽  
Vol 37 (4) ◽  
pp. 1229-1249 ◽  
Author(s):  
De-Xiang Ma ◽  
Wei-Gao Ge
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Point Boundary ◽  
One Dimensional ◽  
The One

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.

scholarly journals Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Nadir Benkaci-Ali
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Fixed Point Index ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Fractional Order Differential Equation ◽  
Infinite Point ◽  
Liouville Derivative

In this paper, we establish the existence of nontrivial positive solution to the following integral-infinite point boundary-value problem involving ϕ-Laplacian operator D0+αϕx,D0+βux+fx,ux=0,x∈0,1,D0+σu0=D0+βu0=0,u1=∫01 gtutdt+∑n=1n=+∞ αnuηn, where ϕ:0,1×R→R is a continuous function and D0+p is the Riemann-Liouville derivative for p∈α,β,σ. By using some properties of fixed point index, we obtain the existence results and give an example at last.

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