Mountain pass solutions to equations of p-Laplacian type

By Pablo De Nápoli, M. Mariani. 2003

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Existence of solutions for p(x)-Laplacian problems on a bounded domain (2005, background): “Whenp(x) is a constant function, there are a lot of studies for the case of bou domains; see, for example, [4,7,8,12,16] and references therein.”
Nonuniformly nonlinear elliptic equations of p-biharmonic type (2008, unknown): “We also extend the results of [6,11,15] to fourth order equation where the problems ∇a(x,∇u)= f (x,u) in Ω with homogeneous Dirichlet boundary conditions are considered.”
Multiple solutions for an eigenvalue problem involving p-Laplacian type operators (2012, background): “1 of [21] and the proof uses a somehow more direct simpler argument.”
Multiple solutions for p-Laplacian type equations (2008, background): “In both papers [3,4], the nonlinear term f : Ω × R → R verifies the Ambrosetti–Rabinowitz type condition: defining F(x, s) = ∫ s 0 f (x, t)dt , there exist s0 > 0 and θ > p such that 0 < θ F(x, s) ≤ s f (x, s), ∀x ∈ Ω , s ∈ R, |s| ≥ s0.”