TY - JOUR

T1 - A priori bounds for positive solutions of a semilinear elliptic equation

AU - Cosner, Chris

AU - Schmitt, Klaus

PY - 1985/9

Y1 - 1985/9

N2 - We consider the semilinear elliptic equation -△u = ƒ(u), x ∈ Ω, subject to zero Dirichlet boundary conditions, where ∈ ⊂ Rn is a bounded domain with smooth boundary and the nonlinearity ƒ assumes both positive and negative values. Under the assumption that ∈ satisfies certain symmetry conditions we establish two results providing lower bounds on the C0(∈̅) norm of positive solutions. The bounds derived are the same one obtains in dimension n = 1.

AB - We consider the semilinear elliptic equation -△u = ƒ(u), x ∈ Ω, subject to zero Dirichlet boundary conditions, where ∈ ⊂ Rn is a bounded domain with smooth boundary and the nonlinearity ƒ assumes both positive and negative values. Under the assumption that ∈ satisfies certain symmetry conditions we establish two results providing lower bounds on the C0(∈̅) norm of positive solutions. The bounds derived are the same one obtains in dimension n = 1.

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U2 - 10.1090/S0002-9939-1985-0796444-0

DO - 10.1090/S0002-9939-1985-0796444-0

M3 - Article

AN - SCOPUS:84864263679

VL - 95

SP - 70

EP - 73

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -