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Multiplicity for Nonlinear Elliptic Boundary Value Problems of p-Laplacian Type without Ambrosetti-Rabinowitz Condition

Author: LiYingHong
Tutor: LiGongBao
School: Central China Normal University
Course: Basic mathematics
Keywords: p - Laplace operator Ambrosetti-Rabinowitz condition Existence Non - trivial solution Four solutions
CLC: O175.8
Type: Master's thesis
Year: 2009
Downloads: 21
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Abstract


In this paper, the following p - the Laplace - type nonlinear elliptic boundary value problems for the existence of multiple solutions for lt ; p lt ; ∞ , Ω ( ? ) R N < / sup> is a smooth bounded domain (?) u p-Laplace operator , and f: Ω × R → R satisfies ( ?) not -Δ p in W 0 < / sub > . 1 p (Ω) the characteristics of value , as well as some other structural conditions . appropriate assumptions , we use the (C) c proved that under the conditions of the non- smooth mountain pass lemma ( * ) There are at least four non- trivial solution (see Theorem 1.3 ) , to promote the of NSPapageorgiou, EMRocha and V.Staicu [ 29 ] one of the main results of as well as GBLi and HSZhou [ 23 ] one of the main results our results [ 29 ] different results that : [ 29] assume that f satisfies the Ambrosetti-Rabinowitz condition , and we assume that f (x, t) at t = ∞ at p - asymptotically linear and does not meet the Ambrosetti-Rabinowitz condition. our results with [ 23] results in a difference in that : [23] , is also assumed that f (x, t) at t = ∞ at the p - asymptotically linear , but [ 23 ] also assumed that x ∈ Ω uniformly , while we do not assume that f (x, t) at t = 0 is p- ultra-linear , i.e., (?) .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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