Existence of sign-changing solutions for the nonlinear $p$-Laplacian boundary value problem

Details Existence of sign-changing solutions for the nonlinear $p$-Laplacian boundary value problem Existence of sign-changing solutions for the nonlinear $p$-Laplacian boundary value problem

2011-05-11

arxiv.org/abs/1105.2187v1

Mathematics

Classical Analysis and ODEs

22 pages

Scientific paper

We study the nonlinear one-dimensional $p$-Laplacian equation $$ -(y'^{(p-1)})'+(p-1)q(x)y^{(p-1)}=(p-1)w(x)f(y) on (0,1),$$ with linear separated boundary conditions. We give sufficient conditions for the existence of solutions with prescribed nodal properties concerning the behavior of $f(s)/s^{(p-1)}$ when $s$ are at infinity and zero. These results are more general and complementary for previous known ones for the case $p=2$ and $q$ is nonnegative.

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