Přejít k obsahu


Positive solutions of critical quasilinear elliptic equations in R^N

Citace: [] BINDING, P., DRÁBEK, P., HUANG, Y. Positive solutions of critical quasilinear elliptic equations in R^N. Mathematica Bohemica, 1999, roč. 124, č. 2-3, s. 149-166.
Druh: ČLÁNEK
Jazyk publikace: eng
Anglický název: Positive solutions of critical quasilinear elliptic equations in R^N
Rok vydání: 1999
Autoři: Paul Binding , Pavel Drábek , Yin Xi Huang
Abstrakt EN: We consider the existence of positive solutions of (1) -\Delta_pu=\lambda g(x)|u|^{p-2}u+\alpha h(x)|u|^{q-2}u+f(x)|u|^{p^*-2}u in R^N where \lambda,\alpha\in R, 1 0 b the principal eigenvalue of (2) -\Delta_pu=\lambda g(x)|u|^{p-2}u in \R^N, \int_{\R^N} g(x)|u|^p>0, with u^+_1>0 the associated eigenfunction. We prove that, if \int_{\R^N} f|u^+_1|^{p^*}<0, \int_{\R^N}h|u^+_1|^q>0 if 1<0 ip\lambda^=_1 and \alpha^*>0, such that for \lambda \in[\lambda^+_1,\lambda^*) and \alpha \in[0,\alpha^*), (1) has at least one positive solution.
Klíčová slova

Zpět

Patička