Properties of the spectrum of an elliptic boundary value problem with a parameter and a discontinuous nonlinearity

2019 ◽  
Vol 210 (7) ◽  
pp. 1043-1066 ◽  
Author(s):  
V. N. Pavlenko ◽  
D. K. Potapov
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Discontinuous Nonlinearity ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value

An elliptic boundary-value problem with a discontinuous nonlinearity

1981 ◽  
Vol 91 (1-2) ◽  
pp. 161-174 ◽  
Author(s):  
G. Keady
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Step Function ◽  
Discontinuous Nonlinearity ◽  
Elliptic Boundary Value Problem ◽  
Heaviside Step Function ◽  
Elliptic Boundary Value ◽  
Image Position ◽  
Special Case

SynopsisWe study the boundary-value problem, for(λ/k,ψ),Here ∆ denotes the Laplacian,His the Heaviside step function and one of A or k is a given positive constant. We defineand usually omit the subscript. Throughout we are interested in solutions with ψ>0 inΩ and hence with λ/=0.In the special case Ω = B(0, R), denoting the explicit exact solutions by ℑe, the following statements are true, (a) The set Aψ, issimply-connected, (b) Along ℑe, the diameter of Aψtendsto zero when the area of Aψ, tends to zero.For doubly-symmetrised solutions in domains Ω such as rectangles, it is shown that the statements (a) and (b) above remain true.

scholarly journals Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hongsen Fan ◽  
Zhiying Deng
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Critical Exponent ◽  
Positive Solution ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problem ◽  
Nontrivial Solutions ◽  
Elliptic Boundary Value ◽  
Existence And Multiplicity

AbstractIn this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.

Sign in / Sign up

Export Citation Format

Share Document