Variational theory and approximation of boundary value problems

1985 ◽  
pp. 140-179 ◽  
Author(s):  
R. E. Showalter
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Variational Theory

scholarly journals Extension of the example by Moore-Nehari

2015 ◽  
Vol 63 (1) ◽  
pp. 115-127
Author(s):  
Armands Gritsans ◽  
Felix Sadyrbaev
Keyword(s):  
Continuous Function ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Positive Continuous Function ◽  
Variational Theory ◽  
Number Of Zeros

Abstract R. Moore and Z. Nehari developed the variational theory for superlinear boundary value problems of the form x'' = p(t) |x|2εx, x(a) = 0 = x(b), where ε > 0 and p(t) is a positive continuous function. They constructed simple example of the equation considered in the interval [0, b] so that the problem had three positive solutions. We show that this example can be extended so that the respective BVP has infinitely many groups of solutions with a presribed number of zeros.

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