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Nodal Solutions of a p ‐Laplacian Equation
Author(s) -
Bartsch Thomas,
Liu Zhaoli,
Weth Tobias
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504015187
Subject(s) - nodal , mathematics , bounded function , domain (mathematical analysis) , p laplacian , laplace operator , combinatorics , pure mathematics , mathematical analysis , anatomy , medicine , boundary value problem
We prove that the p ‐Laplacian problem −Δ p u = f ( x, u) , with u ∈ u ∈ W 0 1 , p ( Ω ) on a bounded domain Ω ⊂ R N , with p > 1 arbitrary, has a nodal solution provided that f : Ω × R → R is subcritical, and f ( x, t ) / ∣ t ∣ p − 2 is superlinear. Infinitely many nodal solutions are obtained if, in addition, f ( x , − t ) = − f ( x, t ). 2000 Mathematics Subject Classification 35J20, 35J65, 58E05.