Arbitrarily small weak solutions for a nonlinear eigenvalue problem in Orlicz–Sobolev spaces

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Infinitely many solutions for a class of nonlinear eigenvalue problem in Orlicz–Sobolev spaces (2011, unknown): “We use in the proof the following auxiliary results (see [3,7]): : → R : (cid:7) ( , ) ( ,ξ) ∈ ¯ Ω × R ( ) := ( ) − λ ( ) ∈ 0 λ ∈ 1 R ∈ Moreover, since Φ is convex, it follows that J is a convex functional, hence J is sequentially weakly lower semi-continuous.”
Quasilinear elliptic non-homogeneous Dirichlet problems through Orlicz-Sobolev spaces (2012, background): “We point out that, by using the above theoretical result, in [29] it was proved the existence of a well determined open interval of positive parameters for which a non-homogeneous Neumann problem admits infinitely many weak solutions in W (1)LΦ(Ω), that strongly converges to zero; see also the paper”