scholarly journals Multiplicity of positive solutions for a semilinear elliptic equation in $R_+^N$ with nonlinear boundary condition

2010 ◽  
Vol 9 (6) ◽  
pp. 1675-1696 ◽  
Author(s):  
Tsung-Fang Wu ◽  
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

scholarly journals Multiple Positive Solutions for Semilinear Elliptic Equations in Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Tsing-San Hsu ◽  
Huei-Li Lin
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic Equations ◽  
Weight Functions ◽  
Multiple Positive Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation in , , where , if , if ), , satisfy suitable conditions, and may change sign in .

Multiple positive solutions for an unbounded Dirichlet boundary problem involving sign-changing weight

2009 ◽  
Vol 139 (6) ◽  
pp. 1297-1325
Author(s):  
Tsung-fang Wu
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Semilinear Elliptic Equation ◽  
Infinite Strip ◽  
Multiple Positive Solutions ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions ◽  
Image Position ◽  
Dirichlet Boundary Problem

We study the multiplicity of positive solutions for the following semilinear elliptic equation:where 1 < q < 2 < p < 2* (2* = 2N/(N − 2) if N ≥ 3, 2* = ∞ if N = 2), the parameters λ, μ ≥ 0, is an infinite strip in ℝN and Θ is a bounded domain in ℝN−1 We assume that fλ(x) = λf+(x) + f−(x) and gμ(x) = a(x) + μb(x), where the functions f±, a and b satisfy suitable conditions.

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