# Bifurcation theorems for nonlinear problems with lack of compactness

Francesca Faraci; Roberto Livrea

Annales Polonici Mathematici (2003)

- Volume: 82, Issue: 1, page 77-85
- ISSN: 0066-2216

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topFrancesca Faraci, and Roberto Livrea. "Bifurcation theorems for nonlinear problems with lack of compactness." Annales Polonici Mathematici 82.1 (2003): 77-85. <http://eudml.org/doc/280183>.

@article{FrancescaFaraci2003,

abstract = {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 $lim_\{λ→0⁺\} ||u_\{λ\}|| = 0$.},

author = {Francesca Faraci, Roberto Livrea},

journal = {Annales Polonici Mathematici},

keywords = {bifurcation point; -Laplacian; critical points},

language = {eng},

number = {1},

pages = {77-85},

title = {Bifurcation theorems for nonlinear problems with lack of compactness},

url = {http://eudml.org/doc/280183},

volume = {82},

year = {2003},

}

TY - JOUR

AU - Francesca Faraci

AU - Roberto Livrea

TI - Bifurcation theorems for nonlinear problems with lack of compactness

JO - Annales Polonici Mathematici

PY - 2003

VL - 82

IS - 1

SP - 77

EP - 85

AB - 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 $lim_{λ→0⁺} ||u_{λ}|| = 0$.

LA - eng

KW - bifurcation point; -Laplacian; critical points

UR - http://eudml.org/doc/280183

ER -

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