scholarly journals Existence and multiplicity of positive solutions for nonlinear boundary value problems driven by the scalar $p$-Laplacian

2004 ◽  
Vol 3 (4) ◽  
pp. 729-756 ◽  
Author(s):  
Michael E. Filippakis ◽  
◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Existence And Multiplicity ◽  
Nonlinear Boundary Value ◽  
Multiplicity Of Positive Solutions

scholarly journals On the relation between interior critical points of positive solutions and parameters for a class of nonlinear boundary value problems

2002 ◽  
Vol 31 (12) ◽  
pp. 751-760
Author(s):  
G. A. Afrouzi ◽  
M. Khaleghy Moghaddam
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Critical Points ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonnegative Solutions ◽  
Nonlinear Boundary Value

We consider the boundary value problem−u″(x)=λf(u(x)),x∈(0,1);u′(0)=0;u′(1)+αu(1)=0, whereα>0,λ>0are parameters andf∈c2[0,∞)such thatf(0)<0. In this paper, we study for the two casesρ=0andρ=θ(ρis the value of the solution atx=0andθis such thatF(θ)=0whereF(s)=∫0sf(t)dt) the relation betweenλand the number of interior critical points of the nonnegative solutions of the above system.

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