Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian

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Multiple solutions for a p(x)-Kirchhoff-type equation with sign-changing nonlinearities (2013, background): “Motivated by the papers [11,12], the properties of p(x)-Kirchhoff Laplace operators in [15] and the ideas introduced in [21,22], the goal of this article is to study the multiplicity of weak solutions for problem (1.”
Multiplicity results for a class of $p(x)$-Kirchhoff type equations with combined nonlinearities (2012, background): “It should be noticed that we do not require the condition (M 1 ) as in [5, 6, 7, 8], for example (M 1 ) is not satisfied when M(t) = tδ−1 for δ > 1, t > 0.”