A semilinear singular Sturm–Liouville equation involving measure data

Wang, Hui

doi:10.1016/j.anihpc.2015.03.001

Wang, Hui

Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 965-1007.

Résumé

Given $α > 0$ and $p > 1$ , let μ be a bounded Radon measure on the interval $(- 1, 1)$ . We are interested in the equation $- {(| x |^{2 α} u^{'})}^{'} + | u |^{p - 1} u = μ$ on $(- 1, 1)$ with boundary condition $u (- 1) = u (1) = 0$ . We establish some existence and uniqueness results. We examine the limiting behavior of three approximation schemes. The isolated singularity at 0 is also investigated.

MR Zbl

DOI : 10.1016/j.anihpc.2015.03.001

Classification : 34B16, 34E99
Mots clés : Singular Sturm–Liouville equation, Semilinear equation, Radon measure, Elliptic regularization, Classification of singularity

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     title = {A semilinear singular {Sturm{\textendash}Liouville} equation involving measure data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {965--1007},
     publisher = {Elsevier},
     volume = {33},
     number = {4},
     year = {2016},
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     zbl = {1347.34040},
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Wang, Hui. A semilinear singular Sturm–Liouville equation involving measure data. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 965-1007. doi : 10.1016/j.anihpc.2015.03.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2015.03.001/

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