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MULTIPLE SOLUTIONS TO DISCRETE BOUNDARY VALUE PROBLEMS FOR THE p-LAPLACIAN WITH POTENTIAL TERMS ON FINITE GRAPHS

박재현|정순영
대한수학회 (The Korean Mathematical Society)|2015.09|대한수학회보 (Bulletin of the KMS)|제52권 제5호|pp. 1517-1533

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참고문헌

키워드

p-Laplacian difference equationdiscrete p-Laplaciandiscrete boundary value problems
주제분류수학

초록

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.

Abstract

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.

참고문헌 (19)

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