Positive solution for fourth-order m-point nonhomogeneous boundary value problems

2009 ◽  
Vol 32 (2) ◽  
pp. 443-452 ◽  
Author(s):  
Hai-Rui Pei ◽  
Jian-Ping Sun
Keyword(s):  
Boundary Value Problems ◽  
Positive Solution ◽  
Fourth Order ◽  
Boundary Value ◽  
Nonhomogeneous Boundary

scholarly journals Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Ramzi S. Alsaedi
Keyword(s):  
Continuous Function ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Global Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution to the following fourth-order value problem:u(4)(x)=a(x)uσ(x),x∈(0,1)with the boundary conditionsu(0)=u(1)=u'(0)=u'(1)=0, whereσ∈(-1,1)andais a nonnegative continuous function on (0, 1) that may be singular atx=0orx=1. We also give the global behavior of such a solution.

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

2006 ◽  
Vol 11 (4) ◽  
pp. 323-329 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Boundary Value Problems ◽  
Positive Solution ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Smooth Bounded Domain ◽  
Elliptic Boundary Value ◽  
Existence Of Positive Solutions

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

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