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arXiv · 1208.0017

On the existence of sign changing bound state solutions of a quasilinear equation

Carmen Cortázar·Marta Garcia-Huidobro·Cecilia Yarur
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Abstract

In this paper we establish the existence of bound state solutions of any given order to $$ Δ_m u +f(u)=0, x\in R^N, N\ge m>1, (P) $$ where $Δ_m u=\nabla\cdot(|\nabla u|^{m-2}\nabla u)$ using the same techniques as in [GST] to establish the existence of a ground state solution to (P). Since our solutions change sign, we assume f is continuous in R. The main point here is that by asking a stronger subcritical assumption (see (f_3)(ii) below) than the one considered in [GST], we are able to adapt their techniques to obtain the existence of bound states with a prescribed number of zeros.

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Carmen Cortázar, Marta Garcia-Huidobro, Cecilia Yarur. 2012-10-01. On the existence of sign changing bound state solutions of a quasilinear equation. https://arxiv.org/abs/1208.0017

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