The multiplicity of solutions and geometry of a nonlinear elliptic equation

• Autorzy: Q-Heung Choi , Sungki Chun , Tacksun Jung
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35P99: None of the above, but in this section
• 35J25: Boundary value problems for second-order elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 120
• Numer: 3
• Strony: 259-270

Daty

wydano

1996

otrzymano

1995-01-04

poprawiono

1996-03-28

Twórcy

autor

Q-Heung Choi

• Department of Mathematics, Inha University, Incheon 402-751, Korea

autor

Sungki Chun

• Department of Mathematics, Inha University, Incheon 402-751, Korea

autor

Tacksun Jung

• Department of Mathematics, Kunsan National University, Kunsan 573-360, Korea

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