Qualitative properties of weighted fourth order elliptic problems

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for higher-order elliptic equations (35J40) Nonlinear boundary value problems for nonlinear elliptic equations (35J66) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

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Entire solutions for a class of fourth-order semilinear elliptic equations with weights
Weighted Sobolev spaces of radially symmetric functions
On Caffarelli-Kohn-Nirenberg-type inequalities for the weighted biharmonic operator in cones
Existence and stability of entire solutions to a semilinear fourth order elliptic problem
The critical dimension for a fourth-order elliptic problem with singular nonlinearity
Classification of solutions of higher order conformally invariant equations
A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
New types of Caffarelli-Kohn-Nirenberg inequalities and applications
Asymptotic expansions for singular solutions of conformal Q-curvature equations
Radial symmetry of entire solutions of a bi-harmonic equation with exponential nonlinearity
Bôcher-type results for the fourth and higher order equations on singular manifolds with conical metrics
Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems
The Gel'fand problem for the biharmonic operator
Further study of entire radial solutions of a biharmonic equation with exponential nonlinearity
Radial entire solutions for supercritical biharmonic equations
Critical exponents, critical dimensions and the biharmonic operator
On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions.
Qualitative properties of entire radial solutions for a biharmonic equation with supercritical nonlinearity
Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation
A Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity
Stable Solutions for the Bilaplacian with Exponential Nonlinearity
Asymptotic behavior at the isolated singularities of solutions of some equations on singular manifolds with conical metrics

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