Publication Date:
2018-08-27
Description:
Symmetry, Vol. 10, Pages 363: Positive Solutions of One-Dimensional p-Laplacian Problems with Superlinearity Symmetry doi: 10.3390/sym10090363 Authors: G.C. Yang Z.Y. Li We study one-dimensional p-Laplacian problems and answer the unsolved problem. Our method is to study the property of the operator, the concavity of the solutions and the continuity of the first eigenvalues. By the above study, the main difficulty is overcome and the fixed point theorem can be applied for the corresponding compact maps. An affirmative answer is given to the unsolved problem with superlinearity. A global growth condition is not imposed on the nonlinear term f. The assumptions of this paper are more general than the usual, thus the existing results cannot be utilized. Some recent results are improved from weak solutions to classical solutions and from p ≥ 2 to p ∈ ( 1 , ∞ ) .
Electronic ISSN:
2073-8994
Topics:
Mathematics
,
Physics
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