The Rotation Number Approach to Eigenvalues of the One‐Dimensional p‐Laplacian with Periodic Potentials

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Extremal values of smallest eigenvalues of Hill's operators with potentials in L 1 balls ✩ (2009, background): “See [15,24], or [25] for a rotation number approach.”
Resonant nonlinear Neumann problems with indefinite weight (2012, methodology): “We must underline that this is not the case if p = 2 (see Section 6) and if N = 1 (ordinary differential equations, see Zhang [43] and Binding-Rynne [6]).”
Continuity in weak topology: higher order linear systems of ODE (2008, background): “Recall from [ 20 ] that for any given α, β ∈ [0 ,π ), the eigenvalues λ = λm(a) of problem (5.1)– (5.2) are determined by”
Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions ✩ (2005, unknown): “Recently, Zhang [13] considered the differential equation ( φp(x ′) )′ + (λ+ q(t))φp(x)= 0 (1.”
Certain classes of potentials for p ‐Laplacian to be non‐degenerate (2005, methodology): “By the results in [17], ũ has exactly (n + 1) zeros on any interval like [t0, t0 + |I|], t0 ∈ R.”
Extremal values of eigenvalues of Sturm-Liouville operators with potentials in L 1 balls (2009, background): “One has the following comparison or monotonicity results for eigenvalues [19].”
Unilateral global bifurcation phenomena and nodal solutions for p-Laplacian ✩ (2012, unknown): “4), where πp = 2π(p−1)1/p p sin(π/p) , α = u′(0) and sinp is the p-sine function (see [9] or [33]).”