Non Local Weighted Fourth Order Equation in Dimension $4$ with Non-linear Exponential Growth

Quantization Effects for a Fourth Order Equation of Exponential Growth in Dimension Four

We investigate the asymptotic behavior as k → +∞ of sequences (uk)k∈N ∈ C (Ω) of solutions of the equations ∆uk = Vke 4uk on Ω, where Ω is a bounded domain of R and limk→+∞ Vk = 1 in C 0 loc (Ω). The corresponding 2-dimensional problem was studied by Brézis-Merle and Li-Shafrir who pointed out that there is a quantization of the energy when blow-up occurs. As shown by Adimurthi, Struwe and the ...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

The Wave Equation in Non-classic Cases: Non-self Adjoint with Non-local and Non-periodic Boundary Conditions

In this paper has been studied the wave equation in some non-classic cases. In the  rst case boundary conditions are non-local and non-periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers,in which two ...

Well-posedness and standing waves for the fourth-order non-linear Schrödinger-type equation

We consider the initial value problem for the fourth-order non-linear Schrödinger-type equation (4NLS) which describes the motion of an isolated vortex filament. In the first part of this note we review some recent results on the time local well-posedness of (4NLS) and give the alternative proof of those results. In the second part of this note we consider the stability of a standing wave solut...

new family of two-parameters iterative methods for non-linear equations with fourth-order convergence

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