The topological degree for (S)<mml:math alttext="$_+$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>+</mml:mo></mml:math>-mappings concerning a nonlinear eigenvalue problem associated with one-dimensional <mml:math alttext="$p$" id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-Laplacian is evaluated. The result is applied to a variational inequality, where the multiple existence of solutions is discussed.

An index formula for the degree of (S)<mml:math alttext="$_+$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>+</mml:mo></mml:math>-mappings associated with one-dimensional <mml:math alttext="$p$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-Laplacian

An index formula for the degree of (S)<svg style="vertical-align:-3.30472pt" height="5.9875002" version="1.1" viewBox="0 0 7.7375002 5.9875002" width="7.7375002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.012,-0,0,-.012,.062,5.887)"><path id="x2B" d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" /></g></svg>-mappings associated with 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

Abstract

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An index formula for the degree of (S)+-mappings associated with one-dimensional p-Laplacian

https://www.hindawi.com/journals/aaa/2004/591312/