Semilinear elliptic problems with mixed Dirichlet–Neumann boundary conditions

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Nehari manifold and existence of positive solutions to a class of quasilinear problems (2005, background): “where W 1,p Γ (Ω) = {u ∈ W (Ω); u|Γ = 0} is the closure of C(1) 0(Ω∪Γ) with respect to the norm of W (Ω) (we refer the reader to the paper by Colorado & Peral [8] for a complete study in the case p = 2).”
Some nonexistence results for positive solutions of elliptic equations in unbounded domains (2004, methodology): “We refer to [16] for the corresponding analysis for Dirichlet BVP and to the recent paper [11] for a blow-up analysis for some mixed problems in bounded domains.”
The Nehari manifold for systems of nonlinear elliptic equations (2006, methodology): “We can refer the reader to [9] for a complete description of this space in the case p = 2.”
A concave—convex elliptic problem involving the fractional Laplacian (2010, background): “This type of diffusion operators arises in several areas such as physics, probability and finance, see for instance [6, 7, 20, 39].”
A critical fractional equation with concave-convex power nonlinearities (2013, methodology): “0 and ε > 0 small enough, .72) Furthermore, by [18, Lemma 3.8] (see also [41, Proposition 22]) it follows that t ε,λ ε ε .77) Indeed from (2.75) we get provided ε is small enough Moreover, the function ] .”