Variational and topological methods for Dirichlet problems with -Laplacian.

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Infinitely many solutions of some nonlinear variational equations (2009, background): “which has been widely studied (see, e.g., [ 14 ] and references therein).”
Nontrivial solutions of superlinear p-Laplacian equations (2009, background): “Such superlinear elliptic boundary value problem has been studied by many authors, see for instance [1, 5 ,10,15,16].”
Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity (2007, background): “1 can be proved by the Mountain Pass Theorem for any p > 1 (see [1] for the case p = 2 and [12] for the case p = 2).”
On superlinear problems without the Ambrosetti and Rabinowitz condition (2010, background): “Since the seminal work of Ambrosetti and Rabinowitz [1], such superlinear elliptic boundary value problem has been studied by many authors, see for instance [7, 8, 9, 15, 19, 23].”
Infinitely many nontrivial solutions for a class of biharmonic equations via variant fountain theorems (2011, background): “From (f1)− (f2) and Proposition 5 in [3], we know that Nf is continuous from L(Ω) to L p p−1 (Ω) and maps bounded sets into bounded sets.”