Bifurcation theorems for nonlinear problems with lack of compactness

• Autorzy: Francesca Faraci , Roberto Livrea
• Języki publikacji: EN

Abstrakty

EN

We deal with a bifurcation result for the Dirichlet problem
⎧$-Δ_{p}u = μ/|x|^{p} |u|^{p-2}u + λf(x,u)$ a.e. in Ω,
⎨
⎩$u_{|∂Ω} = 0$.
Starting from a weak lower semicontinuity result by E. Montefusco, which allows us to apply a general variational principle by B. Ricceri, we prove that, for μ close to zero, there exists a positive number $λ*_{μ}$ such that for every $λ ∈ ]0,λ*_{μ}[$ the above problem admits a nonzero weak solution $u_{λ}$ in $W₀^{1,p}(Ω)$ satisfying $lim_{λ→0⁺} ||u_{λ}|| = 0$.

Kategorie tematyczne

• 35J60: Nonlinear elliptic equations
• 35B32: Bifurcation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2003
• Tom: 82
• Numer: 1
• Strony: 77-85

Daty

wydano

2003

Twórcy

autor

Francesca Faraci

• Dipartimento di Matematica, e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy

autor

Roberto Livrea

• Dipartimento di Matematica, Università di Messina, Salita Sperone 31, 98166 Sant'Agata, Messina, Italy

Identyfikatory

DOI

10.4064/ap82-1-9