A priori estimates of the second derivatives of solutions to nonlinear second-order equations on the boundary of the domain

1978 ◽  
Vol 10 (1) ◽  
pp. 44-53 ◽  
Author(s):  
A. V. Ivanov
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Second Order ◽  
Priori Estimates ◽  
Second Derivatives ◽  
Derivatives Of ◽  
Second Order Equations

A priori estimates of solutions of nonlinear boundary value problems for singular in a phase variable second order differential inequalities

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Ivan Kiguradze
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Second Order ◽  
Phase Variable ◽  
Differential Inequalities ◽  
Nonlinear Boundary Value Problems ◽  
Estimates Of Solutions ◽  
Priori Estimates

Abstract.For singular in a phase variable second order differential inequalities, a priori estimates of positive solutions, satisfying nonlinear nonlocal boundary conditions, are established.

scholarly journals A PRIORI ESTIMATES FOR THE MOTION OF A SELF-GRAVITATING INCOMPRESSIBLE LIQUID WITH FREE SURFACE BOUNDARY

2009 ◽  
Vol 06 (02) ◽  
pp. 407-432 ◽  
Author(s):  
HANS LINDBLAD ◽  
KARL HÅKAN NORDGREN
Keyword(s):  
A Priori Estimates ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
A Priori ◽  
Time Interval ◽  
Surface Boundary ◽  
Priori Estimates ◽  
Moving Domain ◽  
Half Derivatives ◽  
Derivatives Of

In this paper, we prove a priori estimates in Lagrangian coordinates for the equations of motion of an incompressible, inviscid, self-gravitating fluid with free-boundary. The estimates show that on a finite time interval we control five derivatives of the fluid-velocity and five and a half derivatives of the coordinates of the moving domain.

scholarly journals Periodic solutions for second order differential equations with indefinite singularities

2019 ◽  
Vol 9 (1) ◽  
pp. 994-1007 ◽  
Author(s):  
Shiping Lu ◽  
Xingchen Yu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Second Order ◽  
Continuation Theorem ◽  
Second Order Differential Equations ◽  
Priori Estimates ◽  
Negative Constant

Abstract In this paper, the problem of periodic solutions is studied for second order differential equations with indefinite singularities $$\begin{array}{} \displaystyle x''(t)+ f(x(t))x'(t)+\varphi(t)x^m(t)-\frac{\alpha(t)}{x^\mu(t)}+\frac{\beta(t)}{x^y (t)}=0, \end{array}$$ where f ∈ C((0, +∞), ℝ) may have a singularity at the origin, the signs of φ and α are allowed to change, m is a non-negative constant, μ and y are positive constants. The approach is based on a continuation theorem of Manásevich and Mawhin with techniques of a priori estimates.

The spectral theory of second order two-point differential operators: I. A priori estimates for the eigenvalues and completeness

1992 ◽  
Vol 121 (3-4) ◽  
pp. 279-301 ◽  
Author(s):  
John Locker
Keyword(s):  
Differential Operator ◽  
Spectral Theory ◽  
Differential Operators ◽  
A Priori Estimates ◽  
A Priori ◽  
Second Order ◽  
Boundary Values ◽  
Horizontal Strip ◽  
Priori Estimates

SynopsisThis paper is the first part in a four-part series which develops the spectral theory for a two-point differential operator L in L2[0, 1] determined by a second order formal differential operator l = −D2 + pD + q and by independent boundary values B1, B2. The differential operator L is classified as belonging to one of five cases, Cases 1–5, according to conditions satisfied by the coefficients of B1, B2. For Cases 1–4 it is shown that if λ = ρ2 is any eigenvalue of L with ∣ρ∣ sufficiently large, then ρ lies in the interior of a horizontal strip (Cases 1–3) or the interior of a logarithmic strip (Case 4), and in each of these cases the generalised eigenfunctions of L are complete in L2[0, 1].

Sign in / Sign up

Export Citation Format

Share Document