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In this paper, we prove the existence of at least three non- trivial solutions to nonlinear discrete boundary value problems { -△p,wu(x) + V(x)｜u(x)｜q-2u(x) = f(x; u(x)), x ∈ S, u(x) = 0, x ∈ ∂S, involving the discrete p-Laplacian on simple, finite and connected graphs S(S ∪ ∂S,E) with weight ω, where 1 < q < p < ∞. The approach is based on a suitable combine of variational and truncations methods.
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참고문헌 (19)
참고문헌 신청
A. Elmoataz / 2008 / Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing / IEEE Trans. Image Process 17 (7) : 1047 ~ 1060
D. Q. Jiang / 2005 / A generalized upper and lower solution method for singular discrete boundary value problems for the one-dimensional p-Laplacian / J. Appl. Anal 11 (1) :
G. Bonanno / 2009 / Nonlinear difference equations investigated via critical point methods / Nonlinear Anal 70 (9) : 3180 ~ 3186
G. Bonanno / 2014 / Variational methods on finite dimensional Banach spaces and discrete problems / Adv. Nonlinear Stud 14 (4) : 915 ~ 939
J.-H. Kim / / The (p, w)-Laplacian operators on nonlinear networks / Ph.D. / Uni-versity of Sogang
D. Q. Jiang / 2005 / A generalized upper and lower solution method for singular discrete boundary value problems for the one-dimensional p-Laplacian / J. Appl. Anal 11 (1) :
G. Bonanno / 2009 / Nonlinear difference equations investigated via critical point methods / Nonlinear Anal 70 (9) : 3180 ~ 3186
G. Bonanno / 2014 / Variational methods on finite dimensional Banach spaces and discrete problems / Adv. Nonlinear Stud 14 (4) : 915 ~ 939
J.-H. Kim / / The (p, w)-Laplacian operators on nonlinear networks / Ph.D. / Uni-versity of Sogang
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