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Maximum principles and nonexistence results for radial solutions to equations involving p ‐Laplacian
Author(s) -
Adamowicz Tomasz,
Kałamajska Agnieszka
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1280
Subject(s) - mathematics , monotone polygon , eigenvalues and eigenvectors , maximum principle , ode , nonlinear system , mathematical analysis , sign (mathematics) , sequence (biology) , laplace operator , work (physics) , harmonic , p laplacian , constant (computer programming) , pure mathematics , mathematical physics , mathematical optimization , geometry , boundary value problem , physics , quantum mechanics , biology , computer science , programming language , genetics , optimal control , thermodynamics
We obtain the variant of maximum principle for radial solutions of, possibly singular, p ‐harmonic equations of the form\documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}\begin{eqnarray*} -a(|x|)\Delta_{p}(w)+h \left(|x|, w, \nabla w(x)\cdot\frac{x}{|x|}\right) =\phi(w), \end{eqnarray*}\end{document} as well as for solutions of the related ODE. We show that for the considered class of equations local maxima of | w | form a monotone sequence in | x | and constant sign solutions are monotone. The results are applied to nonexistence and nonlinear eigenvalue problems. We generalize our previous work for the case h ≡0. Copyright © 2010 John Wiley & Sons, Ltd.