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Bifurcation theorems for nonlinear problems with lack of compactness

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Faraci F., Livrea R.

Annales Polonici Mathematici

2003

tom 82

nr 1

77-85

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 $lim_{λ→0⁺} ||u_{λ}|| = 0$.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Faraci F.

1 Livrea R.

1 2003

Wyniki wyszukiwania

Bifurcation theorems for nonlinear problems with lack of compactness