Sign changing solutions for elliptic equations with critical growth in cylinder type domains

Girão, Pedro; Ramos, Miguel

doi:10.1051/cocv:2002061

Girão, Pedro ; Ramos, Miguel

ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002) , pp. 407-419.

Résumé

We prove the existence of positive and of nodal solutions for $- Δ u = {| u |}^{p - 2} u + μ {| u |}^{q - 2} u$ , $u \in H_{0}^{1} (Ω)$ , where $μ > 0$ and $2 < q < p = 2 N (N - 2)$ , for a class of open subsets $Ω$ of $ℝ^{N}$ lying between two infinite cylinders.

MR 1925035

DOI : https://doi.org/10.1051/cocv:2002061
Classification : 35J20, 35J25, 35J65, 35B05
Mots clés : nodal solutions, cylindrical domains, semilinear elliptic equation, critical Sobolev exponent, concentration-compactness

@article{COCV_2002__7__407_0,
     author = {Gir\~ao, Pedro and Ramos, Miguel},
     title = {Sign changing solutions for elliptic equations with critical growth in cylinder type domains},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {407--419},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2002},
     doi = {10.1051/cocv:2002061},
     mrnumber = {1925035},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2002__7__407_0/}
}

Girão, Pedro; Ramos, Miguel. Sign changing solutions for elliptic equations with critical growth in cylinder type domains. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002) , pp. 407-419. doi : 10.1051/cocv:2002061. http://www.numdam.org/item/COCV_2002__7__407_0/

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