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Eigenvalue problems for a quasilinear elliptic equation on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\\mathbb{R}^{N}$" id="E1"><mml:mrow><mml:msup><mml:mi>โ</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:mrow></mml:math>
We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation โ ฮ p u = ฮป g ( x )| u | p โ2 u , x โ โ N , lim | x |โ+ โ u ( x ) = 0, where ฮ โฆ