Existence results for resonant perturbations of the Fučik spectrum

The Beginning of the Fučik Spectrum for the p-Laplacian

“…Part of the argument here is adapted from [13,11]. Let us first recall the precise meaning of the fact that the inequalities (5.3) holds uniformly with respect to x: for any =>0 there exists a = (x) # L 1 (0) such that for a.e.…”

Nonresonance conditions on the potential with respect to the Fučík spectrum for semilinear Dirichlet problems

“…In 2000, Schechter [19] studied the existence of solutions of problem (1.1) when f is resonant with respect to Σ, i.e., the limits in (1.3) and (1.4) exist with (μ, ν) ∈ C l,1 or (μ, ν) ∈ C l,2 . Usually, such solvability conditions require that the ratio f (x,s) s stays asymptotically at infinity between two consecutive branches of Σ (see [2,5,10,11,[14][15][16][17][18][19] and the related references). In this paper, inspiring from [4], we obtain the existence of solutions of problem (1.1) by requiring that f is of linear growth at infinity and the ratio 2F (x,s) s 2 stays asymptotically at infinity away from the Fučík spectrum.…”

One-Sided Resonance Problems for Quasilinear Elliptic Operators

“…One excellent example of a resonance result for the PDE case is found in [7], where the boundary value problem…”

“…Throughout the section we assume (F-1)-(F-3), (A-1)-(A-2), (g-1)-(g-2), (a-1)-(a-3) and let be given by (7). For w ∈ W with w < 0 we have w = − A x w − G x w − Hw.…”