Existence and Multiplicity of Positive Solutions For a Class of Elliptic Boundary Value Problems in the Half-Space

2007 ◽  
Vol 7 (2) ◽  
Author(s):  
Tsing-San Hsu
Keyword(s):  
Boundary Value Problems ◽  
Half Space ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

AbstractIn this paper, we prove that if b(x) satisfies some suitable conditions, then -Δu + u = b(x)u

scholarly journals Multiplicity of positive solutions to semilinear elliptic boundary value problems

1999 ◽  
Vol 4 (3) ◽  
pp. 195-208
Author(s):  
Kenichiro Umezu
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Degree Theory ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions ◽  
Ordered Banach Spaces

We study semilinear elliptic boundary value problems of one parameter dependence where the number of positive solutions is discussed. Our main purpose is to characterize the critical value given by the infimum of such parameters for which positive solutions exist. Our approach is based on super- and sub-solutions, and relies on the topological degree theory on the positive cones of ordered Banach spaces. A concrete example is also presented.

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