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The partial differential equation u_(xy)+(N(u_x+u_y))/(x+y)=0.

A curvature of a submanifold of a manifold which depends on its particular embedding. Examples of extrinsic curvature include the curvature and torsion of curves in ...

The system of partial differential equations u_(xx)-u_(yy)+/-sinucosu+(cosu)/(sin^3u)(v_x^2-v_y^2)=0 (v_xcot^2u)_x=(v_ycot^2u)_y.

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...

A function used to study ordinary differential equations.

A boundary value problem is a problem, typically an ordinary differential equation or a partial differential equation, which has values assigned on the physical boundary of ...

The partial differential equation (1+f_y^2)f_(xx)-2f_xf_yf_(xy)+(1+f_x^2)f_(yy)=0 (Gray 1997, p. 399), whose solutions are called minimal surfaces. This corresponds to the ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

A differential equation or system of ordinary differential equations is said to be autonomous if it does not explicitly contain the independent variable (usually denoted t). ...