Multiple solutions for some elliptic equations with a nonlinearity concave at the origin

• Published in: Nonlinear analysis Vol. 66; no. 12; pp. 2940 - 2946
• Main Authors: de Paiva, Francisco Odair, Massa, Eugenio
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 15.06.2007; Elsevier
• Subjects: Calculus of variations and optimal control; Concave nonlinearity; Exact sciences and technology; Mathematical analysis; Mathematics; Multiplicity of solution; Partial differential equations; Sciences and techniques of general use; Variational methods; Multiplicity of solution; Variational methods; Concave nonlinearity; Multiple solution; Elliptic equation; Multiplicity; Nonlinear analysis; Mathematical model
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2006.04.015

In this paper we establish the existence of multiple solutions for the semilinear elliptic problem − Δ u = − λ | u | q − 2 u + a u + g ( u ) in  Ω u = 0 on  ∂ Ω , where Ω ⊂ R N is a bounded domain with smooth boundary ∂ Ω , g : R → R is a function of class C 1 such that g ( 0 ) = g ′ ( 0 ) = 0 , λ > 0 is a real parameter, a ∈ R , and 1 < q < 2 .