Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domains

@article{Zhu1990ExistenceOM,
  title={Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domains},
  author={Xiping Zhu and Huan-Song Zhou},
  journal={Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={1990},
  volume={115},
  pages={301-318}
}
  • Xiping Zhu, Huan-Song Zhou
  • Published 1990
  • Mathematics
  • Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
By using the concentration-compactness method of Lions [14, 16] and the mountain pass theorem of Ambrosetti and Rabinowitz [3], through a careful inspection of the energy balance for some sequence of approximated solutions, we show that under suitable conditions on f and h, the inhomogeneous problem. −Δu + c2u = λ(f(u) + h(x)) for x ∈ Ω (Ω is an exterior domain in ℝN, N≧ 3) and has at least two positive solutions. 
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    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2003
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References

SHOWING 1-10 OF 18 REFERENCES
A perturbation method in critical point theory and applications
This paper is concerned with existence and multiplicity results for nonlinear elliptic equations of the type -Au = |u|''_1u + h(x) in P», u = 0 on 3s. Here, s c R^ is smooth and bounded, and h e
Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
Soit Ω un domaine borne dans R n avec n≥3. On etudie l'existence d'une fonction u satisfaisant l'equation elliptique non lineaire -Δu=u P +f(x,u) sur Ω, u>0 sur Ω, u=0 sur ∂Ω, ou p=(n+2)/(n−2),
On the Existence of Positive Solutions of Semilinear Elliptic Equations
In this paper we study the existence of positive solutions of semilinear elliptic equations. Various possible behaviors of nonlinearity are considered, and in each case nearly optimal multiplicity
Nonconvex minimization problems
I. The central result. The grandfather of it all is the celebrated 1961 theorem of Bishop and Phelps (see [7], [8]) that the set of continuous linear functionals on a Banach space E which attain
On the existence of positive entire solutions of a semilinear elliptic equation
AbstractUnder suitable hypotheses we obtain various theorems concerning the existence of positive solutions of the equation $$\Delta u{\text{ }} - {\text{ }}u{\text{ }} + {\text{
Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
This paper gives a survey over some of the most important methods and results of nonlinear functional analysis in ordered Banach spaces. By means of iterative techniques and by using topological
Bifurcation in Lp(RN) for a Semilinear Elliptic Equation
Keywords: $Lsp p$-bifurcation ; constrained ; minimization ; Sobolev spaces ; nonlinear eigenvalue problem ; semilinear ; spectrum ; linearisation ; variational ; structure Reference
Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
Abstract : Continuation and variational methods are developed to construct positive solutions for nonlinear elliptic eigenvalue problems. The class of equations studied contain in particular models
...
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