We present sharp lower bounds for eigenvalues of the one-dimensional <mml:math alttext="$p$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-Laplace operator. The method of proof is rather elementary, based on a suitable generalization of the Lyapunov inequality.

Lower bounds for eigenvalues of the one-dimensional <mml:math alttext="$p$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-Laplacian

Lower bounds for eigenvalues of the one-dimensional <svg style="vertical-align:-3.50804pt" height="13.3" version="1.1" viewBox="0 0 10.2 13.3" width="10.2" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,8.863)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36&#xA;t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" /></g></svg>-Laplacian

Abstract and Applied Analysis

Lower bounds for eigenvalues of the one-dimensional p-Laplacian

Abstract

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