Multiple positive solutions for a p-Laplace Benci-Cerami type problem (1 < p < 2), via Morse theory

被引：0
|
作者：
Vannella, Giuseppina [1 ]
机构：
[1] Politecn Bari, Dipartimento Meccan Matemat & Management, Via Orabona 4, I-70125 Bari, Italy
来源：
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2023年 / 25卷 / 02期
关键词：
p-Laplace equations; perturbation results; Morse theory; critical groups; NONTRIVIAL SOLUTIONS; ELLIPTIC PROBLEMS; EQUATIONS; EXISTENCE; FUNCTIONALS;
D O I：
10.1142/S0219199721500656
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let us consider the quasilinear problem(P-epsilon) {-epsilon(p) Delta(p)u + u(p-1) = f(u) in Omega,u > 0 in Omega,u = 0 on theta Omega,where Omega is a bounded domain in R-N with smooth boundary, N >= 2, 1 < p < 2, epsilon > 0 is a parameter and f : R -> R is a continuous function with f(0) = 0, having a subcritical growth. We prove that there exists epsilon(*) > 0 such that, for every epsilon is an element of (0, epsilon(*)), (P-epsilon) has at least 2P(1)(Omega) -1 solutions, possibly counted with their multiplicities, where P-t(Omega) is the Poincare polynomial of Omega. Using Morse techniques, we furnish an interpretation of the multiplicity of a solution, in terms of positive distinct solutions of a quasilinear equation on Omega, approximating (P-epsilon).
引用
收藏
页数：20
相关论文
共 49 条
  • [21] Multiple solutions for the p-Laplacian equations with concave nonlinearities via Morse theory
    Sun, Mingzheng
    Su, Jiabao
    Cai, Hongrui
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2017, 19 (03)
  • [22] Holder estimate for a tug-of-war game with 1 &lt; p &lt; 2 from Krylov-Safonov regularity theory
    Arroyo, Angel
    Parviainen, Mikko
    REVISTA MATEMATICA IBEROAMERICANA, 2024, 40 (03) : 1023 - 1044
  • [23] Solutions of an infinite system of integral equations of Volterra-Stieltjes type in the sequence spaces lp(1 &lt; p &lt; ∞) and c0
    Samadi, Ayub
    Avini, M. Mosaee
    Mursaleen, M.
    AIMS MATHEMATICS, 2020, 5 (04): : 3791 - 3808
  • [24] C1,α local regularity for the solutions of the p-laplacian on the Heisenberg group for 2 ≤ p &lt; 1+√5
    Marchi, S
    ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2001, 20 (03): : 617 - 636
  • [25] One-bit block sparse signal recovery via nonconvex l2/lp(0 &lt; p &lt; 1)-minimization
    Chen, Jieqiong
    Gao, Yi
    Li, Jianxi
    Wang, Jianjun
    JOURNAL OF ELECTRONIC IMAGING, 2022, 31 (06)
  • [26] Existence and iteration of positive solutions for a three-point boundary value problem of second order integro-differential equation with p-Laplace operator
    Ma D.-X.
    Hu J.-X.
    Journal of Applied Mathematics and Computing, 2012, 39 (1-2) : 333 - 343
  • [27] Equazioni a derivate parziali. - Monotonicity and symmetry of solutions of p-Laplace equations, 1 less than or equal p less than or equal 2, via the moving plane method
    Damascelli, Lucio
    Pacella, Filomena
    Ambrosetti, A.
    Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni, 9 (02): : 95 - 100
  • [28] Multiple positive solutions of a (p1, p2)-Laplacian system with nonlinear BCs
    Cianciaruso, Filomena
    Pietramala, Paolamaria
    BOUNDARY VALUE PROBLEMS, 2015,
  • [29] Multiple solutions for a BVP on (0,+infinity) via Morse theory and H-0,p(1)(R+)versus C-p(1)(R+) local minimizers
    Ait-Mahiout, K.
    Djebali, S.
    Moussaoui, T.
    ARABIAN JOURNAL OF MATHEMATICS, 2016, 5 (01) : 9 - 22
  • [30] ON OPTIMAL CONTROL PROBLEM FOR AN ILL-POSED STRONGLY NONLINEAR ELLIPTIC EQUATION WITH p-LAPLACE OPERATOR AND L1 -TYPE OF NONLINEARITY
    Kogut, Peter, I
    Kupenko, Olha P.
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (03): : 1273 - 1295
12345