Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 256, Issue 7, Pages 2449-2479Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2014.01.010
Keywords
Nonlinear regularity; Nonlinear maximum principle; Robin p-Laplacian; Nodal and constant sign solutions; Extremal solutions; Morse theory
Categories
Funding
- CNCS [PCE-47/2011]
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We consider a parametric nonlinear Robin problem driven by the p-Laplacian. We show that if the parameter lambda > (lambda) over cap (2) = the second eigenvalue of the Robin p-Laplacian, then the problem has at least three nontrivial solutions, two of constant sign and the third nodal. In the semilinear case (p = 2), we show that we can generate a second nodal solution. Our approach uses variational methods, truncation and perturbation techniques, and Morse theory. In the process we produce two useful remarks about the first two eigenvalues of the Robin p-Laplacian. (C) 2014 Elsevier Inc. All rights reserved.
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