A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

DOI10.15388/namc.2020.25.15736zbMath1433.35108OpenAlexW2998771394MaRDI QIDQ5212515

Yujun Cui, Li Shan Liu, Yong-Hong Wu, Xin Guang Zhang

Publication date: 29 January 2020

Published in: Nonlinear Analysis: Modelling and Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.15388/namc.2020.25.15736

zbMATH Keywords

\(k\)-Hessian equationblow-up radial solutions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Monge-Ampère equations (35J96)

Related Items (42)

Monotonicity and symmetry of solutions to fractional Laplacian in strips ⋮ Entire positive \(k\)-convex solutions to \(k\)-Hessian type equations and systems ⋮ Positive solutions of singular \(k_i\)-Hessian systems ⋮ Existence and asymptotic behaviour of entire large solutions for \(k\)-Hessian equations ⋮ Existence of positive solutions for third-order semipositone boundary value problems on time scales ⋮ The uniqueness and iterative properties of solutions for a general Hadamard-type singular fractional turbulent flow model ⋮ The radial solution for an eigenvalue problem of singular augmented Hessian equation ⋮ Monotone iterative method for fractional differential equations with integral boundary conditions ⋮ Uniqueness of iterative positive solution to nonlinear fractional differential equations with negatively perturbed term ⋮ New sequential fractional differential equations with mixed-type boundary conditions ⋮ Multiplicity of quasilinear Schrödinger equation ⋮ Analytical solutions to the Caudrey-Dodd-Gibbon-Sawada-Kotera equation via symbol calculation approach ⋮ Results of positive solutions for the fractional differential system on an infinite interval ⋮ A relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem ⋮ Existence of solutions for fractional boundary value problems with a quadratic growth of fractional derivative ⋮ The existence and multiplicity of \(k\)-convex solutions for a coupled \(k\)-Hessian system ⋮ A fixed-point theorem for ordered contraction-type decreasing operators in Banach space with lattice structure ⋮ Inelastic interaction and blowup new solutions of nonlinear and dispersive long gravity waves ⋮ Nonlinear \(n\)-order \(m\)-point semipositive boundary value problems and applications ⋮ A necessary and sufficient condition for the existence of entire large solutions to a \(k\)-Hessian system ⋮ Existence and uniqueness of positive solutions for singular nonlinear fractional differential equation via mixed monotone operator method ⋮ Positive solutions for a weakly singular Hadamard-type fractional differential equation with changing-sign nonlinearity ⋮ The existence of positive solution of a nonlinear problem on unit circle ⋮ 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 ⋮ On highly dimensional elastic and nonelastic interaction between internal waves in straight and varying cross-section channels ⋮ Solutions for a singular Hadamard-type fractional differential equation by the spectral construct analysis ⋮ Iterative properties of solution for a general singular \(n\)-Hessian equation with decreasing nonlinearity ⋮ Existence of positive solutions for second-order third-point semipositive BVP ⋮ Extremal solutions for a class of tempered fractional turbulent flow equations in a porous medium ⋮ An SDP method for copositivity of partially symmetric tensors ⋮ Exact analytical solutions of generalized fifth-order KdV equation by the extended complex method ⋮ The eigenvalue problem of a singular \(k\)-Hessian equation ⋮ Existence and nonexistence of positive solutions for high-order fractional differential equation boundary value problems at resonance ⋮ Boundary blow-up solutions to the \(k\)-Hessian equation with the logarithmic nonlinearity and singular weights ⋮ Classification and existence of positive entire \(k\)-convex radial solutions for generalized nonlinear \(k\)-Hessian system ⋮ Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain ⋮ On the exact solutions of two \((3+1)\)-dimensional nonlinear differential equations ⋮ Multiple solutions for a modified quasilinear Schrödinger elliptic equation with a nonsquare diffusion term ⋮ On a power-type coupled system of k-Hessian equations

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