The multiplicity of solutions and geometry of a nonlinear elliptic equation
Studia Mathematica, Tome 120 (1996) no. 3, pp. 259-270
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let Ω be a bounded domain in $ℝ^n$ with smooth boundary ∂Ω and let L denote a second order linear elliptic differential operator and a mapping from $L^2(Ω)$ into itself with compact inverse, with eigenvalues $-λ_{i}$, each repeated according to its multiplicity, 0 λ_{1} λ_{2} λ_{3} ≤ ... ≤ λ_{i} ≤ ... → ∞. We consider a semilinear elliptic Dirichlet problem $Lu+bu^+-au^-=f(x)$ in Ω, u=0 on ∂ Ω. We assume that $a λ_{1}$, $λ_{2} b λ_{3}$ and f is generated by $ϕ_{1}$ and $ϕ_{2}$. We show a relation between the multiplicity of solutions and source terms in the equation.
@article{10_4064_sm_120_3_259_270,
author = {Q-Heung Choi},
title = {The multiplicity of solutions and geometry of a nonlinear elliptic equation},
journal = {Studia Mathematica},
pages = {259--270},
publisher = {mathdoc},
volume = {120},
number = {3},
year = {1996},
doi = {10.4064/sm-120-3-259-270},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-120-3-259-270/}
}
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Q-Heung Choi. The multiplicity of solutions and geometry of a nonlinear elliptic equation. Studia Mathematica, Tome 120 (1996) no. 3, pp. 259-270. doi: 10.4064/sm-120-3-259-270
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