The multiplicity of solutions and geometry of a nonlinear elliptic equation

Choi, Q.; Chun, Sungki; Jung, Tacksun

Studia Mathematica, Tome 119 (1996), p. 259-270 / Harvested from The Polish Digital Mathematics Library

Résumé

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 < λ1 < λ2 < λ3 ≤ ... ≤ λi ≤ ... → ∞. We consider a semilinear elliptic Dirichlet problem $L u + b u^{+} - a u^{-} = f (x)$ 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.

Publié le : 1996-01-01

Zbl 0869.35039

EUDML-ID : urn:eudml:doc:216336

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     title = {The multiplicity of solutions and geometry of a nonlinear elliptic equation},
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     volume = {119},
     year = {1996},
     pages = {259-270},
     zbl = {0869.35039},
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Choi, Q.; Chun, Sungki; Jung, Tacksun. The multiplicity of solutions and geometry of a nonlinear elliptic equation. Studia Mathematica, Tome 119 (1996) pp. 259-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv120i3p259bwm/

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