Geodesic
Nonlinear semigroup approach to the Hamilton-Jacobi equation -- a toy model
Minimax theory and its applications, Tome 8 (2023) no. 1
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We discuss the existence and multiplicity problem of viscosity solution to the Hamilton-Jacobi equation h(x,dxu) + λ(x)u = c, x ∈ M, where M is a closed manifold and λ : M → R changes signs on M, via nonlinear semigroup method. It turns out that a bifurcation phenomenon occurs when the parameter c strides over some critical value. As an application of the main result, we analyse the structure of the set of viscosity solutions of an one-dimensional example in detail.
Mots-clés : Hamilton-Jacobi equations, viscosity solutions, bifurcation phenomenon 
@article{MTA_2023_8_1_a2,
     author = {Liang Jin and Jun Yan and Kai Zhao},
     title = {Nonlinear semigroup approach to the {Hamilton-Jacobi} equation -- a toy model},
     journal = {Minimax theory and its applications},
     year = {2023},
     volume = {8},
     number = {1},
     zbl = {1514.35110},
     url = {http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a2/}
}
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Liang Jin; Jun Yan; Kai Zhao. Nonlinear semigroup approach to the Hamilton-Jacobi equation -- a toy model. Minimax theory and its applications, Tome 8 (2023) no. 1. http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a2/