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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. ČLÁNEK eng Positive solutions of critical quasilinear elliptic equations in R^N 1999 Paul Binding , Pavel Drábek , Yin Xi Huang 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.

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