3 results
Steady states of thin-film equations with van der Waals force with mass constraint
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- European Journal of Applied Mathematics / Volume 34 / Issue 2 / April 2023
- Published online by Cambridge University Press:
- 30 May 2022, pp. 280-302
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We consider steady states with mass constraint of the fourth-order thin-film equation with van der Waals force in a bounded domain which leads to a singular elliptic equation for the thickness with an unknown pressure term. By studying second-order nonlinear ordinary differential equation,
we prove the existence of infinitely many radially symmetric solutions. Also, we perform rigorous asymptotic analysis to identify the blow-up limit when the steady state is close to a constant solution and the blow-down limit when the maximum of the steady state goes to the infinity.
\begin{equation*}h_{rr}+\frac{1}{r}h_{r}=\frac{1}{\alpha}h^{-\alpha}-p\end{equation*}
On a singular semilinear elliptic problem with an asymptotically linear nonlinearity
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- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 1 / February 2016
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- 11 December 2015, pp. 59-77
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- February 2016
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Infinitely many arbitrarily small solutions for singular elliptic problems with critical Sobolev–Hardy exponents
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- Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 1 / February 2009
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- 02 February 2009, pp. 97-108
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Let Ω ⊂ ℝN be a bounded domain such that 0 ∈ Ω, N ≥ 3, 2*(s) = 2(N − s)/(N − 2), 0 ≤ s < 2,
. We obtain the existence of infinitely many solutions for the singular critical problem 
with Dirichlet boundary condition for suitable positive number λ.
. We obtain the existence of infinitely many solutions for the singular critical problem 
with Dirichlet boundary condition for suitable positive number λ.