Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614897 | Journal of Mathematical Analysis and Applications | 2016 | 13 Pages |
Abstract
In this paper, we investigate the structure of the nontrivial solution set for the following nonlinear operator equationu=L(λ)u+H(λ,u),(λ,u)∈Rm×X, where m is a positive integer, X is a Banach space, L(⋅):X→XL(⋅):X→X is a (positively) homogeneous compact operator and H:Rm×X→XH:Rm×X→X is compact with H=o(‖u‖)H=o(‖u‖) near u=0u=0 uniformly on bounded λ sets. We obtain some results involving (unilateral) global bifurcation. Two examples of p-Laplacian problem with jumping nonlinearity and nonlocal boundary value problem are given to demonstrate how the theory can be applied.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Guowei Dai,