A biharmonic equation with singular nonlinearity

DOI10.1017/S0013091510000234zbMath1237.35044arXiv0911.0308OpenAlexW2963760781MaRDI QIDQ3116824

Marius Ghergu

Publication date: 12 February 2012

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.0308

zbMATH Keywords

integral equationGreen functionbiharmonic operatorsingular nonlinearity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for higher-order elliptic equations (35J40) Positive solutions to PDEs (35B09) Green's functions for elliptic equations (35J08)

Related Items (11)

Unnamed Item ⋮ Unnamed Item ⋮ Some remarks on biharmonic elliptic problems with a singular nonlinearity ⋮ Uniqueness of weak solutions for a biharmonic problem ⋮ Positive radial solutions for quasilinear biharmonic equations ⋮ Multiple solutions for fourth order elliptic problems with p(x)-biharmonic operators ⋮ A nonlinear bilaplacian equation with hinged boundary conditions and very weak solutions: analysis and numerical solution ⋮ Multiplicity results for the biharmonic equation with singular nonlinearity of super exponential growth in \(\mathbb{R}^4\) ⋮ Existence and global analytic bifurcation for singular biharmonic equation with Navier boundary condition ⋮ Eigenvalues for a fourth order elliptic problem ⋮ On a fourth order elliptic problem with a \(p(x)\)-biharmonic operator

Cites Work

• Unnamed Item
• Unnamed Item
• Estimates for Green function and Poisson kernels of higher-order Dirichlet boundary value problems
• Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions
• Obtuse cones in Hilbert spaces and applications to partial differential equations
• On the structure of biharmonic functions satisfying the clamped plate conditions on a right angle
• Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
• Elliptic partial differential equations of second order
• Sign change for the Green function and for the first eigenfunction of equations of clamped-plate type
• A partial differential equation arising in conformal mapping
• Optimal estimates from below for biharmonic Green functions
• On a dirichlet problem with a singular nonlinearity
• An Elementary Proof That the Biharmonic Green Function of an Eccentric Ellipse Changes Sign
• Regularity of an elliptic problem with a singular nonlinearity
• On 'anti'-eigenvalues for elliptic systems and a question of McKenna and Walter
• Positivity for Perturbations of Polyharmonic Operators with Dirichlet Boundary Conditions in Two Dimensions
• Regions of positivity for polyharmonic Green functions in arbitrary domains
• ISOLATION OF SINGULARITIES OF THE GREEN'S FUNCTION

This page was built for publication: A biharmonic equation with singular nonlinearity