Displaying similar documents to “Boundary singularities of solutions of sublinear elliptic equations.”

A new method to obtain decay rate estimates for dissipative systems with localized damping.

Patrick Martínez (1999)

Revista Matemática Complutense

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We consider the wave equation damped with a locally distributed nonlinear dissipation. We improve several earlier results of E. Zuazua and of M. Nakao in two directions: first, using the piecewise multiplier method introduced by K. Liu, we weaken the usual geometrical conditions on the localization of the damping. Then thanks to some new nonlinear integral inequalities, we eliminate the usual assumption on the polynomial growth of the feedback in zero and we show that the energy of the...

An elliptic semilinear equation with source term involving boundary measures: the subcritical case.

Marie Françoise Bidaut-Véron, Laurent Vivier (2000)

Revista Matemática Iberoamericana

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We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain Ω of RN (N ≥ 2), ⎧   Δu + uq = 0,   in Ω ⎨ ⎩   u = μ,      on ∂Ω where 1 < q < (N + 1)/(N - 1) and μ is a Radon measure on ∂Ω. We give a priori estimates and existence results. The lie on the study of superharmonic functions in some weighted...

Uniqueness of positive solutions of nonlinear second order systems.

Robert Dalmasso (1995)

Revista Matemática Iberoamericana

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In this paper we discuss the uniqueness of positive solutions of the nonlinear second order system -u'' = g(v), -v'' = f(u) in (-R,R), u(±R) = v(±R) = 0 where f and g satisfy some appropriate conditions. Our result applies, in particular, to g(v) = v, f(u) = u, p > 1, or f(u) = λu + au + ... + au, with p > 1, a > 0 for j = 1, ..., k and 0 ≤ λ < μ where μ = π/4R.