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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2019 In the theory of ordinary differential equations, the Clairaut equation is well known. This equation is a non-linear differential equation unresolved with respect to the derivative.
Liliya Leonidovna Ryskina
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Subharmonic Solutions in Singular Systems
Journal of Differential Equations, 1996 The authors consider the problem of bifurcation of periodic solutions in singular systems of differential equations \[ \varepsilon\dot{u}=f(u)+\varepsilon g(t,u,\varepsilon)\quad u\in\mathbb{R}^n, \] where \(g(t+2,u,\varepsilon)=g(t,u,\varepsilon)\) and \(\dot{u}=f(u)\) has an orbit \(\gamma(t)\) homoclinic to a hyperbolic equilibrium point \(p\).
Battelli, Flaviano, Fečkan, Michal
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Some remarks on singular solutions of nonlinear elliptic equations. I [PDF]
, 2009 The paper concerns singular solutions of nonlinear elliptic ...
Caffarelli, Luis +2 more
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Mathematics, 2021 The boundary value problem for the steady Navier–Stokes system is considered in a 2D multiply-connected bounded domain with the boundary having a power cusp singularity at the point O.
Kristina Kaulakytė +1 more
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Singular solution to Special Lagrangian Equations
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010 We prove the existence of non-smooth solutions to three-dimensional Special Lagrangian Equations in the non-convex case. Résumé Nous démontrons l'existence de solutions singulières d'équations speciales lagrangiennes en dimension trois, dans le cas non convexe.
Nadirashvili, Nikolai, Vlăduţ, Serge
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Singular standing-ring solutions of nonlinear partial differential equations
, 2009 We present a general framework for constructing singular solutions of nonlinear evolution equations that become singular on a d-dimensional sphere, where d>1. The asymptotic profile and blowup rate of these solutions are the same as those of solutions of
Bricmont +30 more
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Twin Solutions to Singular Dirichlet Problems
Journal of Mathematical Analysis and Applications, 1999 The authors consider the Dirichlet second-order boundary value problem \[ y''+ \phi(t)[g(y(t))+ h(y(t))]= 0,\quad 0< t< 1,\quad y(0)= y(1)= 0,\tag{1} \] and establish the existence of two solutions \(y_1,y_2\in C[0,1]\cap C^2(0, 1)\) with \(y_1> 0\), \(y_2> 0\) on \((0,1)\). The nonlinearity in (1) may be singular at \(y= 0\), \(t= 0\) and/or \(t= 1\).
Agarwal, R.P., O'Regan, D.
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Singular solutions to a quasilinear {ODE}
Advances in Differential Equations, 2005 7
DALBONO, Francesca +1 more
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Singular Solutions to Monge-Ampère Equation
Analysis in Theory and Applications, 2022 We construct merely Lipschitz and $C^{1,α}$ with rational $α ∈ (0, 1 − 2/n]$ viscosity solutions to the Monge-Ampère equation with constant right hand side.
Caffarelli, Luis A., Yuan, Yu
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Singular solutions of fractional order conformal Laplacians
, 2011 We investigate the singular sets of solutions of conformally covariant elliptic operators of fractional order with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe ...
Gonzalez, Maria del Mar +2 more
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