The eigenvalue problem of a singular \(k\)-Hessian equation

DOI10.1016/j.aml.2021.107666zbMath1479.35590OpenAlexW3201198853MaRDI QIDQ2060925

Pengtao Xu, Xin Guang Zhang, Yong-Hong Wu

Publication date: 13 December 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107666

zbMATH Keywords

Schauder's fixed point theoremsingularityupper-lower solutions\(k\)-Hessian equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Nonlinear elliptic equations (35J60)

Related Items (16)

Existence and multiplicity of radial solutions for a \(k\)-Hessian system ⋮ Entire positive \(k\)-convex solutions to \(k\)-Hessian type equations and systems ⋮ Positive solutions of singular \(k_i\)-Hessian systems ⋮ Existence of positive solutions for third-order semipositone boundary value problems on time scales ⋮ Non-degeneracy and uniqueness of the radial solutions to a coupled \(k\)-Hessian system ⋮ Existence and multiplicity of radially symmetric \(k\)-admissible solutions for a \(k\)-Hessian equation ⋮ Existence of \(k\)-convex solutions for the \(k\)-Hessian equation ⋮ A necessary and sufficient condition for the existence of entire large solutions to a \(k\)-Hessian system ⋮ Existence results for the \(k\)-Hessian type system with the gradients via \(\mathbb{R}_+^n\)-monotone matrices ⋮ Entire positive \(p\)-\(k\)-convex radial solutions to \(p\)-\(k\)-Hessian equations and systems ⋮ The Riccati-Bernoulli subsidiary ordinary differential equation method to the coupled Higgs field equation ⋮ A class of singular \(k_{i}\)-Hessian systems ⋮ Existence of positive solutions for a singular Hessian equation with a negative augmented term ⋮ The extreme solutions for a σ‐Hessian equation with a nonlinear operator ⋮ The iterative properties of solutions for a singular k-Hessian system ⋮ Radial symmetry and monotonicity of the positive solutions for \(k\)-Hessian equations

Cites Work

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• Bounded solutions of a \(k\)-Hessian equation in a ball
• Existence and nonexistence theorem for entire subsolutions of \(k\)-Yamabe type equations
• Hessian measures. I
• Existence and asymptotic properties of solutions for a nonlinear Schrödinger elliptic equation from geophysical fluid flows
• Hessian measures. II
• The convergence analysis and uniqueness of blow-up solutions for a Dirichlet problem of the general \(k\)-Hessian equations
• Radial solutions of a nonlinear \(k\)-Hessian system involving a nonlinear operator
• On the Dirichlet problem for Monge-Ampère type equations
• Necessary and sufficient conditions on solvability for Hessian inequalities
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations
• A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator
• Boundary blow-up solutions to the \(k\)-Hessian equation with singular weights
• The existence and nonexistence of entire large solutions for a quasilinear Schrödinger elliptic system by dual approach

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