Geodesic
Multiplicity of Positive Solutions for an Anisotropic Problem via Sub-Supersolution Method and Mountain Pass Theorem
Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1363-1374
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We use the sub-supersolution method and the Mountain Pass Theorem in order to show existence and multiplicity of solution for an anisotropic problem given by \begin{equation*} \begin{cases} \ -\Big[\displaystyle\sum^{N}_{i=1}\frac{\partial}{\partial x_{i}} \Big( \Big\vert \frac{\partial u}{\partial x_{i}}\Big\vert^{pi-2} \frac{\partial u}{\partial x_{i}}\Big )\ \Big]=a(x)u+ h(x,u) \mbox{ in } \Omega\mbox{,}\\[1mm] \ u>0\mbox{ in }\Omega, \quad u=0\mbox{ on } \partial\Omega\mbox{.} \end{cases} \end{equation*} We also prove the uniqueness of the solution for the linear anisotropic problem, a Comparison Principle for the anisotropic operator and a regularity result.
Classification : 35J60, 35J66
Mots-clés : Anisotropic operator, sub-supersolution method, Mountain Pass Theorem 
@article{JCA_2020_27_4_JCA_2020_27_4_a15,
     author = {G. C. G. dos Santos and G. Figueiredo and J. R. S. Silva},
     title = {Multiplicity of {Positive} {Solutions} for an {Anisotropic} {Problem} via {Sub-Supersolution} {Method} and {Mountain} {Pass} {Theorem}},
     journal = {Journal of convex analysis},
     pages = {1363--1374},
     year = {2020},
     volume = {27},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a15/}
}
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G. C. G. dos Santos; G. Figueiredo; J. R. S. Silva. Multiplicity of Positive Solutions for an Anisotropic Problem via Sub-Supersolution Method and Mountain Pass Theorem. Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1363-1374. http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a15/