Increasing radial solutions for Neumann problems without growth restrictions
Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 4, p. 573-588
We study the existence of positive increasing radial solutions for superlinear Neumann problems in the ball. We do not impose any growth condition on the nonlinearity at infinity and our assumptions allow for interactions with the spectrum. In our approach we use both topological and variational arguments, and we overcome the lack of compactness by considering the cone of nonnegative, nondecreasing radial functions of H 1 (B).
Nous étudions lʼexistence de solutions radiales positives croissantes de problèmes de Neumann super linéaires dans la boule. Nous nʼimposons aucune restriction de croissance sur la non linéarité à lʼinfini et nos hypothèses permettent également une interaction avec le spectre. Notre approche combinne des arguments topologiques et variationnels. Nous contournons le manque de compacité en travaillant dans le cône des fonctions radiales, positives et croissantes de H 1 (B).
DOI : https://doi.org/10.1016/j.anihpc.2012.02.002
Keywords: Supercritical problems, Krasnoselʼskiĭ fixed point, Invariant cone, Gradient flow
@article{AIHPC_2012__29_4_573_0,
     author = {Bonheure, Denis and Noris, Benedetta and Weth, Tobias},
     title = {Increasing radial solutions for Neumann problems without growth restrictions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {29},
     number = {4},
     year = {2012},
     pages = {573-588},
     doi = {10.1016/j.anihpc.2012.02.002},
     zbl = {1248.35079},
     mrnumber = {2948289},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2012__29_4_573_0}
}
Bonheure, Denis; Noris, Benedetta; Weth, Tobias. Increasing radial solutions for Neumann problems without growth restrictions. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 4, pp. 573-588. doi : 10.1016/j.anihpc.2012.02.002. http://www.numdam.org/item/AIHPC_2012__29_4_573_0/

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