Shibo Liu

activity

20122026

most citedExistence results for fractional p-Laplacian problems via Morse theory

6 citations · 11 across the 19 of their papers we have counts for

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math.AP2026

On biharmonic equations with $p$ -Laplacian and indefinite potentials or critical nonlinearity

Shibo Liu, Kanishka Perera

In this paper we consider nonlinear biharmonic equations with $p$ -Laplacian ( $p \geq 2$ ) of the form $$ \left\{ \begin{array}{l} Δ^2 u - Δ_p u + V (x) u = f (x, u) \text{,} u \in H^2…

math.GM2026

Physical derivation of the coarea formula and an elementary proof via gradient flow

Shibo Liu

In this note, we derive an elementary version of the coarea formula by considering the mass of a solid body with density $g (x)$ . Then we present an rigorous proof using the changi…

On biharmonic equations with p-Laplacian and indefinite potentials or critical nonlinearity

Physical derivation of the coarea formula and an elementary proof via gradient flow

On biharmonic equations with $p$ -Laplacian and indefinite potentials or critical nonlinearity