Eigenvalue Problems for the p-Laplacian with Indefinite Weights

By M. Cuesta. 2001

135 citations recorded by the source corpus.

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Citations in the corpus

Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity (2007, background): “It is known that there exist a first eigenvalue λ1 = minσ(− p) > 0 and a second eigenvalue λ2 > λ1, both possessing several equivalent variational characterizations (see [2,20,21,3,13,9]).”
Variational and non-variational eigenvalues of the p-Laplacian (2008, background): “The weighted form, with q = 0 and r > 0, is also common in the literature (see, for example, [6], [11] or [14]), so we also state a result in this form, which will be useful below.”
Nontrivial Solutions for p-Laplace Equations with Right-Hand Side Having p-Linear Growth at Infinity (2005, background): “It is also clear that 1 = 1 = 1 = min u∈M u while it follows from the results of Anane (1987), Anane and Tsouli (1996), Cuesta (2001), Drábek and Robinson (1999), and Lindqvist (1990) that 2 = 2 = 2 > 1 and that 1 2 ⋂ − p = ∅ For a matter of convenience, we also set 0 = − .”
Multiple solutions for an eigenvalue problem involving p-Laplacian type operators (2012, unknown): “1 of [18], the infimum in (3.”
Simplicity of the principal eigenvalue for indefinite quasilinear problems (2007, background): “The fact that when q = p any positive critical point of the functional J must be a minimizer has been known under several regularity assumptions either on the domain Ω or on the weight w (see [26], [12]).”
THE EIGENVALUE PROBLEM FOR A SINGULAR QUASILINEAR ELLIPTIC EQUATION (2004, unknown): “This new sequence of eigenvalues was first introduced by [9] and later used in [7, 6] for a = 0, c = p.”