JournalsrmiVol. 11, No. 2pp. 247–267

Uniqueness of positive solutions of nonlinear second order systems

  • Robert Dalmasso

    Equipe EDP, Grenoble, France
Uniqueness of positive solutions of nonlinear second order systems cover
Download PDF

Abstract

In this paper we discuss the uniqueness of positive solutions of the nonlinear second order system u=g(v)–u'' = g(v), v=f(u)–v'' = f (u) in (R,R)(–R,R), u(±R)=v(±R)=0u(±R) = v(±R) = 0 where ff and gg satisfy some appropriate conditions. Our result applies, in particular, to g(v)=vg(v) = v, f(u)=upf(u) = u^p, p>1p>1, or f(u)=λu+a1up1++akupkf(u) = \lambda u + a_1u^{p1} + \cdots + a_ku^{pk} with pj>1p_j > 1, aj>0a_j > 0 for j=1,,kj = 1,\dots , k and 0λ<μ120 ≤ \lambda < \mu_1^2 where μ1=π2/4R2\mu_1 = \pi^2 / 4R^2.

Cite this article

Robert Dalmasso, Uniqueness of positive solutions of nonlinear second order systems. Rev. Mat. Iberoam. 11 (1995), no. 2, pp. 247–267

DOI 10.4171/RMI/172