In this paper we prove the existence of radial solutions having a prescribed number of sign change to the $p$-Laplacian $ \Delta_{p} u+ f(u)= 0 $ on exterior domain of the ball of radius $ R > 0 $ centered at the origin in $ \mathbf{R^{N}} $. The nonlinearity $ f $ is odd and behaves like $ \vert u\vert^{q-1}u $ when $ u $ is large with $ 1<p<q+1 $ and $ f<0 $ on $ (0,\beta) $ , $ f>0 $ on $ (\beta,\infty) $ where $ \beta>0 $. The method is based on a shooting approach, together with a scaling argument.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 1
Year: 2018

DOI: 10.12732/ijam.v31i1.9

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