Nonlinear biharmonic equations with negative exponents
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Publication:2378189
DOI10.1016/j.jde.2008.06.027zbMath1165.35014OpenAlexW2073252244MaRDI QIDQ2378189
Publication date: 7 January 2009
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2008.06.027
Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)
Related Items (31)
On the sub poly-harmonic property for solutions to \((- \Delta)^p u < 0\) in \(\mathbb{R}^n\) ⋮ On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents ⋮ A local pointwise inequality for a biharmonic equation with negative exponents ⋮ On the positive solutions for a perturbed negative exponent problem on \(\mathbb{R}^3\) ⋮ Radial singular solutions for a fourth order equation with negative exponents ⋮ Classification of entire solutions of $(-\Delta )^N u + u^{-(4N-1)}= 0$ with exact linear growth at infinity in $\mathbf {R}^{2N-1}$ ⋮ Gelfand problem and hemisphere rigidity ⋮ Asymptotic behavior of entire radial solutions of a biharmonic problem with negative exponent ⋮ Remarks on Entire Solutions for Two Fourth-Order Elliptic Problems ⋮ Pointwise bounds and blow-up for nonlinear polyharmonic inequalities ⋮ On the integral systems with negative exponents ⋮ Wolff type potential estimates and application to nonlinear equations with negative exponents ⋮ A new proof of I. Guerra's results concerning nonlinear biharmonic equations with negative exponents ⋮ A pointwise inequality for a biharmonic equation with negative exponent and related problems ⋮ Classification of solutions for an integral system with negative exponents ⋮ Liouville type theorems for general integral system with negative exponents ⋮ Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space ⋮ Isolated singularities of polyharmonic inequalities ⋮ Positive radial solutions for quasilinear biharmonic equations ⋮ A note on nonlinear biharmonic equations with negative exponents ⋮ Multiplicity of solutions for a fourth order equation with power-type nonlinearity ⋮ Symmetry and monotonicity of positive solutions for an integral system with negative exponents ⋮ A compactness theorem on Branson's \(Q\)-curvature equation ⋮ Classification of solutions for an integral system with negative exponents on half space ⋮ Reverse conformally invariant Sobolev inequalities on the sphere ⋮ On the $Q$-curvature problem on $\mathbb {S}^3$ ⋮ Higher order conformally invariant equations in \( \mathbb{R}^3 \) with prescribed volume ⋮ Non-radial solutions to a bi-harmonic equation with negative exponent ⋮ Nonexistence of Positive Supersolutions of Nonlinear Biharmonic Equations without the Maximum Principle ⋮ Liouville theorems for fractional and higher-order Hénon–Hardy systems on ℝn ⋮ Existence and uniqueness of positive solutions for singular biharmonic elliptic systems
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