Bifurcation, a-priori bound and negative solutions for the complex Hessian equation

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Other complex differential geometry (53C56) Bifurcations in context of PDEs (35B32)

Cites Work

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Bifurcation and one-sign solutions of the \(p\)-Laplacian involving a nonlinearity with zeros
Solving the degenerate complex Monge-Ampère equation with one concentrated singularity
Radially symmetric boundary value problems for real and complex elliptic Monge-Ampère equations
The Dirichlet problem for a complex Monge-Ampère equation
Counterexamples to regularity for the complex Monge-Ampère equation
The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function
The complex Monge-Ampère equation
Polyharmonic \(k\)-Hessian equations in \(\mathbb{R}^N\)
Existence and convexity of local solutions to degenerate Hessian equations
A Dirichlet's principle for the \(k\)-Hessian
Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities.
The Sobolev inequality for complex Hessian equations
Asymptotic behavior of solutions of a \(k\)-Hessian evolution equation
Some global results for nonlinear eigenvalue problems
Weak solutions to the complex Hessian equation.
Uniqueness theorems for negative radial solutions of \(k\)-Hessian equations in a ball
Existence for a \(k\)-Hessian equation involving supercritical growth
Spectral theory and nonlinear functional analysis
The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
A priori bounds for positive solutions of nonlinear elliptic equations
On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation

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