p-Laplacian problems with jumping nonlinearities

@inproceedings{Rynne2006pLaplacianPW,
  title={p-Laplacian problems with jumping nonlinearities},
  author={Bryan P. Rynne},
  year={2006}
}
We consider the p-Laplacian boundary value problem −(φp(u′(x)))′ = f (x,u(x),u′(x)), a.e. x ∈ (0,1), (1) c00u(0) = c01u′(0), c10u(1) = c11u′(1), (2) where p > 1 is a fixed number, φp(s) = |s|p−2s, s ∈ R, and for each j = 0,1, |cj0| + |cj1| > 0. The function f : [0,1] × R2 → R is a Carathéodory function satisfying, for (x, s, t) ∈ [0,1] × R2, ψ±(x)φp(s) − E(x, s, t) f (x, s, t) Ψ±(x)φp(s) + E(x, s, t), ±s 0, where ψ±, Ψ± ∈ L1(0,1), and E has the form E(x, s, t) = ζ(x)e(|s|+|t |), with ζ ∈ L1(0,1… CONTINUE READING
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