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The multiplicity of solutions and geometry of a nonlinear elliptic equation

Q. Choi; Sungki Chun; Tacksun Jung — 1996

Studia Mathematica

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....

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Currently displaying 1 – 5 of 5

The multiplicity of solutions and geometry of a nonlinear elliptic equation

An application of category theory to a class of the systems of the superquadratic wave equations.

Nontrivial solutions of the asymmetric beam system with jumping nonlinear terms.

Existence of four solutions of some nonlinear Hamiltonian system.

Critical point theory applied to a class of the systems of the superquadratic wave equations.