Singular solutions to \(k\)-Hessian equations with fast-growing nonlinearities

DOI10.1016/j.na.2022.113000zbMath1494.35024arXiv2106.11235OpenAlexW3176245548WikidataQ113868545 ScholiaQ113868545MaRDI QIDQ2145656

João Marcos Bezerra do Ó, Esteban da Silva, Evelina Shamarova

Publication date: 17 June 2022

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.11235

zbMATH Keywords

singular solutionbifurcation diagrams\(k\)-Hessian equationLiouville-Bratu-Gelfand problemnumber of intersection pointsmultiplicity of regular solutions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Bifurcations in context of PDEs (35B32) Quasilinear elliptic equations (35J62) Methods of ordinary differential equations applied to PDEs (35A24) Quasilinear elliptic equations with (p)-Laplacian (35J92)

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Touchdown solutions in general MEMS models ⋮ Existence results for the \(k\)-Hessian type system with the gradients via \(\mathbb{R}_+^n\)-monotone matrices ⋮ The extreme solutions for a σ‐Hessian equation with a nonlinear operator

Cites Work

• Unnamed Item
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• Bounded solutions of a \(k\)-Hessian equation in a ball
• Generalized Joseph-Lundgren exponent and intersection properties for supercritical quasilinear elliptic equations
• Existence and multiplicity for negative solutions of \(k\)-Hessian equations
• Bounded solutions of a \(k\)-Hessian equation involving a weighted nonlinear source
• The Liouville-Bratu-Gelfand problem for radial operators
• A generalized Pohozaev identity and its applications
• Remarks on critical exponents for Hessian operators
• Stability of steady states of the Cauchy problem for the exponential reaction-diffusion equation
• Symmetry and related properties via the maximum principle
• Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
• The Dirichlet problem for Hessian equations on Riemannian manifolds
• Positive singular solutions for semilinear elliptic equations with supercritical growth
• On the Dirichlet problem for Hessian equations
• A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth
• Semilinear elliptic equations and supercritical growth
• Singular solutions of elliptic equations with iterated exponentials
• Radial single point rupture solutions for a general MEMS model
• Classification of bifurcation diagrams for elliptic equations with exponential growth in a ball
• Non-linear heat generation and stability of the temperature distribution in conducting solids
• Bifurcation and admissible solutions for the Hessian equation
• The Yamabe problem for higher order curvatures
• Quasilinear Dirichlet problems driven by positive sources
• Uniqueness theorems for negative radial solutions of \(k\)-Hessian equations in a ball
• Existence for a \(k\)-Hessian equation involving supercritical growth
• Stable solutions to semilinear elliptic equations are smooth up to dimension \(9\)
• Geometry of phase space and solutions of semilinear elliptic equations in a ball
• Positive solutions of elliptic equations involving supercritical growth
• FURTHER STUDIES OF EMDEN'S AND SIMILAR DIFFERENTIAL EQUATIONS
• Regularity of the extremal solution of semilinear elliptic equations
• A bifurcation diagram of solutions to an elliptic equation with exponential nonlinearity in higher dimensions
• On Nonexistence of type II blowup for a supercritical nonlinear heat equation
• A variational theory of the Hessian equation
• Some problems in the theory of quasilinear equations
• Nonlinear diffusion induced by nonlinear sources
• Membrane buckling: A study of solution multiplicity