Boundary blow-up in nonlinear elliptic equations of Bieberbach–Rademacher type

DOI10.1090/S0002-9947-07-04107-4zbMath1134.35039arXivmath/0506121OpenAlexW2076227737MaRDI QIDQ3431214

Florica-Corina St. Cîrstea, Vicenţiu D. Rădulescu

Publication date: 5 April 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506121

zbMATH Keywords

large solutionsboundary blow-upregular variation theory

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60)

Related Items (54)

Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term ⋮ Asymptotic behavior of boundary blow-up solutions to elliptic equations ⋮ Asymptotic behavior of entire large solutions to semilinear elliptic equations ⋮ Existence and global asymptotic behavior of singular positive solutions for radial Laplacian ⋮ Boundary asymptotic and uniqueness of solutions to the \(p\)-Laplacian with infinite boundary values ⋮ Blow-up rate of the unique solution for a class of one-dimensional equations with a weakly superlinear nonlinearity ⋮ Asymptotic behaviour of Hessian equation with boundary blow up ⋮ Boundary blow-up elliptic problems of Bieberbach and Rademacher type with nonlinear gradient terms ⋮ Blow-up rate of the unique solution for a class of one-dimensional \(p\)-Laplacian equations ⋮ Large solutions to non-divergence structure semilinear elliptic equations with inhomogeneous term ⋮ Necessary and sufficient conditions for the existence of large solutions to semilinear elliptic equations with gradient terms ⋮ The existence of infinitely many boundary blow-up solutions to the \(p\)-\(k\)-Hessian equation ⋮ SHARP ASYMPTOTIC ANALYSIS OF POSITIVE SOLUTIONS OF A COMBINED STURM-LIOUVILLE PROBLEM ⋮ Boundary behavior of large solutions to the infinity Laplace equations on the half-line ⋮ Boundary blow-up solutions of \(p\)-Laplacian elliptic equations with lower order terms ⋮ The first and second expansion of large solutions for quasilinear elliptic equations with weight functions ⋮ Uniqueness of boundary blow-up solutions on unbounded domain of \(\mathbb R^N\) ⋮ The second order expansion of boundary blow-up solutions for infinity-Laplacian equations ⋮ Blow-up rates and uniqueness of large solutions for elliptic equations with nonlinear gradient term and singular or degenerate weights ⋮ Asymptotics for singular solutions of quasilinear elliptic equations with an absorption term ⋮ Large solution to nonlinear elliptic equation with nonlinear gradient terms ⋮ Solutions ofp-Laplace Equations with Infinite Boundary Values: The case of Non-Autonomous and Non-Monotone Nonlinearities ⋮ Entire large solutions to semilinear elliptic equations with rapidly or regularly varying nonlinearities ⋮ Combined effects in singular elliptic problems in punctured domain ⋮ Singular solutions of a nonlinear equation in a punctured domain of \(\mathbb{R}^{2}\) ⋮ Blow-up rates of large solutions for infinity Laplace equations ⋮ Refined second boundary behavior of the unique strictly convex solution to a singular Monge-Ampère equation ⋮ The second expansion of the unique vanishing at infinity solution to a singular elliptic equation ⋮ Boundary asymptotic and uniqueness of solution for a problem with \(p(x)\)-Laplacian ⋮ The exact asymptotic behavior of boundary blow-up solutions to infinity Laplacian equations ⋮ Boundary blow-up quasilinear elliptic problems of the Bieberbach type with nonlinear gradient terms ⋮ The second expansion of large solutions for semilinear elliptic equations ⋮ On boundary blow-up solutions to equations involving the \(\infty \)-Laplacian ⋮ Boundary behavior of solutions for the degenerate logistic type elliptic problem with boundary blow-up ⋮ The exact blow-up rates of large solutions for semilinear elliptic equations ⋮ Boundary blow-up rates of large solutions for elliptic equations with convection terms ⋮ Boundary asymptotic behavior and uniqueness of large solutions to quasilinear elliptic equations ⋮ Uniqueness results and asymptotic behavior of solutions with boundary blow-up for logistic-type porous media equations ⋮ On a singular \(k\)-Hessian equation ⋮ Boundary blow-up solutions to the Monge-Ampère equation: sharp conditions and asymptotic behavior ⋮ On a \(k\)-Hessian equation with a weakly superlinear nonlinearity and singular weights ⋮ Asymptotic behavior of large solutions to \(p\)-Laplacian of Bieberbach-Rademacher type ⋮ Entire large solutions to the \(k\)-Hessian equations with weights: existence, uniqueness and asymptotic behavior ⋮ Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain ⋮ Boundary behavior of large solutions for semilinear elliptic equations with weights ⋮ On the critical behavior for inhomogeneous wave inequalities with Hardy potential in an exterior domain ⋮ Boundary behaviour for solutions of boundary blow-up problems in a borderline case ⋮ Asymptotic behavior of large solution to elliptic equation of Bieberbach-Rademacher type with convection terms ⋮ Lifespan of solutions to semilinear damping wave equations in De Sitter spacetime ⋮ On the moving plane method for boundary blow-up solutions to semilinear elliptic equations ⋮ Boundary blow-up solutions to degenerate elliptic equations with non-monotone inhomogeneous terms ⋮ Blow-up solutions to the Monge-Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates ⋮ Asymptotic behavior of large solution for boundary blowup problems with non-linear gradient terms ⋮ Positive solutions of semilinear problems in an exterior domain of \(\mathbb{R}^2\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A probabilistic approach to one class of nonlinear differential equations
• On the inequality \(\Delta u \geqq f (u)\)
• Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs
• Asymptotic behavior of solutions of boundary blow-up problems
• `Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
• Asymptotic behaviour of large solutions of quasilinear elliptic problems
• Positive solutions of an elliptic partial differential equation on \(\mathbb{R}^N\)
• Uniqueness of the blow-up boundary solution of logistic equations with absorbtion.
• Extremal singular solutions for degenerate logistic-type equations in anisotropic media
• Asymptotic behavior of positive solutions of some elliptic problems.
• Some remarks on classical problems and fine properties of Sobolev spaces
• On the solvability of a semilinear elliptic equation via an associated eigenvalue problem
• 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)
• Remarks on sublinear elliptic equations
• On a problem of Bieberbach and Rademacher
• Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations
• Sur un mode de croissance régulière. Théorèmes fondamentaux
• Regularly varying functions

This page was built for publication: Boundary blow-up in nonlinear elliptic equations of Bieberbach–Rademacher type