The boundary blow-up rate of large solutions.

DOI10.1016/j.jde.2003.06.003zbMath1130.35329OpenAlexW1991923279MaRDI QIDQ1416452

Julián López-Gómez

Publication date: 14 December 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2003.06.003

zbMATH Keywords

large solutionsblowing-up ratesvanishing weight at variable rates

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Boundary values of solutions to elliptic equations and elliptic systems (35J67)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the inequality \(\Delta u \geqq f (u)\)
• Dual semigroups and second order linear elliptic boundary value problems
• Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs
• Scalar curvature and conformal deformation of hyperbolic space
• Semilinear elliptic equations with uniform blow-up on the boundary
• `Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
• Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations
• Uniqueness of the blow-up boundary solution of logistic equations with absorbtion.
• Asymptotics for the blow-up boundary solution of the logistic equation with absorption.
• The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems
• Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equations
• On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems.
• Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up
• EXISTENCE AND UNIQUENESS OF BLOW-UP SOLUTIONS FOR A CLASS OF LOGISTIC EQUATIONS
• On solutions of δu=f(u)
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Remarks on sublinear elliptic equations
• On the Positive Solutions of Semilinear Equations Δu + λu - hu p = 0 on the Compact Manifolds
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• Positive solutions of a semilinear elliptic equation on a compact manifold
• The boundary trace and generalized boundary value problem for semilinear elliptic equations with coercive absorption
• Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations
• Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems.
• On the existence and numerical computation of classical and non-classical solutions for a family of elliptic boundary value problems

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