Open AccessPositive solutions with changing sign energy to a nonhomogeneous elliptic problem of fourth order
Author(s) -
Mohamed Talbi,
Najib Tsouli
Publication year - 2011
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.v29i1.11491
Subject(s) - lambda , multiplicative function , mathematics , sign (mathematics) , order (exchange) , nonlinear system , mathematical analysis , elliptic curve , mathematical physics , physics , quantum mechanics , finance , economics
SPM: www.spm.uem.br/spm doi:10.5269/bspm.v29i1.11491 Positive solutions with changing sign energy to a nonhomogeneous elliptic problem of fourth order M.Talbi and N.Tsouli abstract: In this paper, we study the existence for two positive solutions to a nonhomogeneous elliptic equation of fourth order with a parameter λ such that 0 < λ < λ̂. The first solution has a negative energy while the energy of the second one is positive for 0 < λ < λ0 and negative for λ0 < λ < λ̂. The values λ0 and λ ̂ are given under variational form and we show that every corresponding critical point is solution of the nonlinear elliptic problem (with a suitable multiplicative term)