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This article concerns the existence and multiplicity of solutions for the singular p-biharmonic problem involving the Hardy potential and the critical Hardy-Sobolev exponent. To this end we use variational methods combined with the Mountain pass theorem and the Ekeland variational principle. We illustrate the usefulness of our results with and example. [ABSTRACT FROM AUTHOR]

This article concerns the nonhomogeneous Klein-Gordon-Maxwell equation -Δu + u - (2w + Φ) Φu + |u|p-1u + h(x), in ℝ³; ΔΦ = (w + Φ)u², in ℝ³, where w > 0 is constant, p ∈ (1; 5). Under appropriate assumptions on h(x), the existence of at least two solutions is obtained by applying the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. [ABSTRACT FROM AUTHOR]