Multiple solutions for singular N-Laplace equations with a sign changing nonlinearity

J. Tyagi

doi:10.3934/cpaa.2013.12.2381

Article Contents

2013, Volume 12, Issue 6: 2381-2391. Doi: 10.3934/cpaa.2013.12.2381

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Multiple solutions for singular N-Laplace equations with a sign changing nonlinearity

J. Tyagi^1,

1.
Indian Institute of Technology Gandhinagar, Vishwakarma Government Engineering College Complex, Chandkheda, Visat-Gandhinagar Highway, Ahmedabad, Gujarat, 382424

Received: October 31, 2011

Revised: August 31, 2012

Published: October 2013

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Abstract

In this article, we prove the existence of multiple weak solutions to N-Laplace equation \begin{eqnarray} -\Delta_N u-\mu \frac{g(x)}{(|x| \log\frac{R}{|x|})^N }|u|^{N-2}u=\lambda f(x,u), \ in\ \Omega.\\ u =0, \ on\ \partial \Omega, \end{eqnarray} using Bonanno's three critical point theorem.

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Mathematics Subject Classification: Primary: 35J20; Secondary: 35J75.

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