Boundary value problems for second-order nonlinear difference equations with discrete phi-Laplacian and singular phi
(2008) Journal of Difference Equations and Applications — Vol. 14, n° 10-11, p. 1099-1118 (2008)
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- Abstract
- In this article, we study the existence and multiplicity of solutions for boundary value problems of the type del[phi(Delta x(k))] + f(k)(x(k), Delta x(k)) = 0 (2 <= k <= n-1), l(x, Delta x) = 0, where phi : (-a, a) -> R denotes an increasing homeomorphism such that phi(0) = 0 and 0 < a < infinity, l(x, Delta x) = 0 denotes the Dirichlet, periodic or Neumann boundary conditions and f(k) (2 <= k <= n - 1) are continuous functions. Our main tool is Brouwer degree together with fixed point reformulations of the above problems.
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Bereanu, C., & Mawhin, J. (2008). Boundary value problems for second-order nonlinear difference equations with discrete phi-Laplacian and singular phi. Journal of Difference Equations and Applications, 14(10-11), 1099-1118. https://doi.org/10.1080/10236190802332290 (Original work published 2008)