On a class of two-dimensional singular elliptic problems

2001 ◽  
Vol 131 (3) ◽  
pp. 479-497 ◽  
Author(s):  
Paolo Caldiroli ◽  
Roberta Musina
Keyword(s):  
Positive Solutions ◽  
Exterior Domain ◽  
Elliptic Problems ◽  
Two Dimensional ◽  
Dirichlet Problems ◽  
Existence Of Positive Solutions

We consider Dirichlet problems of the form −|x|αΔu = λu + g(u) in Ω, u = 0 on ∂Ω, where α, λ ∈ R, g ∈ C(R) is a superlinear and subcritical function, and Ω is a domain in R2. We study the existence of positive solutions with respect to the values of the parameters α and λ, and according that 0 ∈ Ω or 0 ∈ ∂Ω, and that Ω is an exterior domain or not.

On a class of two-dimensional singular elliptic problems

2001 ◽  
Vol 131 (3) ◽  
pp. 479-497 ◽  
Author(s):  
Paolo Caldiroli ◽  
Roberta Musina
Keyword(s):  
Positive Solutions ◽  
Exterior Domain ◽  
Elliptic Problems ◽  
Two Dimensional ◽  
Dirichlet Problems ◽  
Existence Of Positive Solutions

We consider Dirichlet problems of the form −|x|αΔu = λu + g(u) in Ω, u = 0 on ∂Ω, where α, λ ∈ ℝ, g ∈ C(ℝ) is a superlinear and subcritical function, and Ω is a domain in ℝ2. We study the existence of positive solutions with respect to the values of the parameters α and λ, and according that 0 ∈ Ω or 0 ∈ ∂Ω, and that Ω is an exterior domain or not.

scholarly journals Positive Solution for the Elliptic Problems with Sublinear and Superlinear Nonlinearities

2010 ◽  
Vol 2010 ◽  
pp. 1-10
Author(s):  
Chunmei Yuan ◽  
Shujuan Guo ◽  
Kaiyu Tong
Keyword(s):  
Variational Method ◽  
Positive Solution ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Problems ◽  
Real Parameter ◽  
Existence Of Positive Solutions

This paper deals with the existence of positive solutions for the elliptic problems with sublinear and superlinear nonlinearities-Δu=λa(x)up+b(x)uqinΩ,u>0inΩ,u=0on∂Ω, whereλ>0is a real parameter,0<p<1<q.Ωis a bounded domain inRN  (N≥3), anda(x)andb(x)are some given functions. By means of variational method and super-subsolution method, we obtain some results about existence of positive solutions.

scholarly journals Positive solutions of critical quasilinear elliptic problems in general domains

1998 ◽  
Vol 3 (1-2) ◽  
pp. 65-84 ◽  
Author(s):  
Filippo Gazzola
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Unbounded Domains ◽  
Critical Growth ◽  
Quasilinear Elliptic Equations ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

We consider a certain class of quasilinear elliptic equations with a term in the critical growth range. We prove the existence of positive solutions in bounded and unbounded domains. The proofs involve several generalizations of standard variational arguments.

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