Steven D. Taliaferro

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math.AP2014

Nonexistence of Positive Supersolutions of Nonlinear Biharmonic Equations without the Maximum Principle

Marius Ghergu, Steven D. Taliaferro

We study classical positive solutions of the biharmonic inequality $- Δ^{2} v \geq f (v)$ in exterior domains in $R^{n}$ where $f : (0, \infty) \to (0, \infty)$ is continuous functio…

math.AP2014

Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities

Marius Ghergu, Steven D. Taliaferro

We study the behavior near the origin of $C^{2}$ positive solutions $u (x)$ and $v (x)$ of the system $0 \leq - Δ u \leq (\frac{1}{∣ x ∣ ^{α}} * v)^{λ}$ $0 \leq - Δ v \leq (\frac{1}{∣ x ∣ ^{β}} * u)^{σ}$ in $B_…

math.AP2010

Isolated Singularities of Polyharmonic Inequalities

Marius Ghergu, Amir Moradifam, Steven D. Taliaferro

We study nonnegative classical solutions $u$ of the polyharmonic inequality $- Δ^{m} u > 0$ in a punctured neighborhood of the origin in $R^{n}$ . We give necessary and sufficient condit…