Abstract
A class of nonlinear equations −(rn−1|u′|p−2u′)′=rn−1w(r)f(u)on [0,1], where 1<p<∞, is considered. We study the existence of sign-changing solutions to this problem. Some sufficient conditions for such solutions with the prescribed number of zeros are developed. We generalize the result of Naito and Tanaka (2008) to the radial solutions of a class of nonlinear p-Laplacian equations in Rn. Some related issues on the half-line will be also discussed.
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