Geodesic
Existence of solutions for quasilinear parabolic equations at resonance
Electronic journal of differential equations, Tome 2013 (2013)
In this article, we show the existence of nontrivial solutions for a class of quasilinear parabolic differential equations. To obtain the solution in a weighted Sobolev space, we use the Galerkin method, Brouwer's theorem, and a compact Sobolev-type embedding theorem proved by Shapiro.
Classification : 35H30, 35K58, 65L60
Keywords: weighted Sobolev space, quasilinear parabolic equation, resonance 
@article{EJDE_2013__2013__a5,
     author = {Jia,  Gao and Zhang,  Xiao-Juan and Huang,  Li-Na},
     title = {Existence of solutions for quasilinear parabolic equations at resonance},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1288.35303},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a5/}
}
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Jia,  Gao; Zhang,  Xiao-Juan; Huang,  Li-Na. Existence of solutions for quasilinear parabolic equations at resonance. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a5/