In this paper, we investigate the local and global nature for the connected components of positive solutions set of an elliptic equation with nonlocal terms. The local bifurcation results of positive solutions are obtained by using the local bifurcation theory, Lyapunov-Schmidt reduction technique, etc. Under suitable conditions, we show two proofs of priori estimates by using blow-up technique, upper and lower solution method, etc. Finally, the global bifurcation results of positive solutions are obtained by using priori bounds, global bifurcation theory.
Citation: Jiaqing Hu, Xian Xu, Qiangqiang Yang. Bifurcation results of positive solutions for an elliptic equation with nonlocal terms[J]. AIMS Mathematics, 2021, 6(9): 9547-9567. doi: 10.3934/math.2021555
In this paper, we investigate the local and global nature for the connected components of positive solutions set of an elliptic equation with nonlocal terms. The local bifurcation results of positive solutions are obtained by using the local bifurcation theory, Lyapunov-Schmidt reduction technique, etc. Under suitable conditions, we show two proofs of priori estimates by using blow-up technique, upper and lower solution method, etc. Finally, the global bifurcation results of positive solutions are obtained by using priori bounds, global bifurcation theory.
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Jiaqing Hu, Xian Xu, Qiangqiang Yang. Bifurcation results of positive solutions for an elliptic equation with nonlocal terms[J]. AIMS Mathematics, 2021, 6(9): 9547-9567. doi: 10.3934/math.2021555
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