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1
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On the multiplicity of critical points for parameterized functionals on reflexive Banach spaces

100%
Anello G.
Studia Mathematica
|
2012
|
tom 213
|
nr 1
49-60
EN
Some general multiplicity results for critical points of parameterized functionals on reflexive Banach spaces are established. In particular, one of them improves some aspects of a recent result by B. Ricceri. Applications to boundary value problems are also given.
2
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On some elliptic boundary-value problems with discontinuous nonlinearities

100%
Anello G.
Annales Polonici Mathematici
|
2005
|
tom 86
|
nr 3
283-290
EN
We establish two existence results for elliptic boundary-value problems with discontinuous nonlinearities. One of them concerns implicit elliptic equations of the form ψ(-Δu) = f(x,u). We emphasize that our assumptions permit the nonlinear term f to be discontinuous with respect to the second variable at each point.
3
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An existence and localization theorem for the solutions of a Dirichlet problem

64%
Anello G., Cordaro G.
Annales Polonici Mathematici
|
2004
|
tom 83
|
nr 2
107-112
EN
We establish an existence theorem for a Dirichlet problem with homogeneous boundary conditions by using a general variational principle of Ricceri.
4
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Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions

64%
Anello G., Cubiotti P.
Annales Polonici Mathematici
|
2004
|
tom 83
|
nr 2
179-187
EN
We consider a multifunction $F:T×X → 2^E$, where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.
5
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Infinitely many positive solutions for the Neumann problem involving the p-Laplacian

64%
Anello G., Cordaro G.
Colloquium Mathematicum
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2003
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tom 97
|
nr 2
221-231
EN
We present two results on existence of infinitely many positive solutions to the Neumann problem ⎧ $-Δ_{p}u + λ(x)|u|^{p-2}u = μf(x,u)$ in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where $Ω ⊂ ℝ^{N}$ is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, $λ ∈ L^{∞}(Ω)$ with $essinf_{x∈Ω} λ(x) > 0$ and f: Ω × ℝ → ℝ is a Carathéodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.
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