Consider the boundary value problem left { textstylebegin{array}{l} -mathscr{D}_{mathbf{t}}^{beta}v(t)=r(t), quad tin 0,1), v(0)=v(1)=0.
Consider the periodic boundary value problem left { textstylebegin{array}l} ddot{u}(t)+ r u t-tau)+nabla F(t, u t-tau))=0, quad mbox{a.e.
Let (e=e(x)) be the solution of the following boundary value problem: left { textstylebegin{array}{l} L varphi(x)=1, quad xinOmega, Bvarphi=0, quad xinpartial Omega.
Consider the periodic boundary value problem left { textstylebegin{array}{ll} ddot{u}(t)+r u t-tau)+nabla F(t, u t-tau))=0, quadmbox{a.e.
Consider the Neumann boundary value problem left { textstylebegin{array}{l} -Delta^{2} u t-1)+L u t-1h(t),quad tin[1,T]_{mathbf{Z}}, Delta u(0)=Delta u(T)=0.
Then the boundary value problem left { textstylebegin{array}{l} -Delta^{2}psi k-1)=f_{2k}(0,psi k)),quad kinmathbb{Z}(1,N), psi(0)=psi(N+1)=0 end{array}displaystyle right.
The Lyapunov inequality states that a necessary condition for the boundary value problem left { begin{array}{l} y"(t) + q(t y(t) = 0,quad a < t < b, y(a)=0=y(b) end{array} right.
We consider the following singularly perturbed elliptic boundary value problem: left { textstylebegin{array}l} Lu x,y equivvarepsilon^{2}Delta u x,y)=f u,x,y),quad (x,y inOmega, u x,y)|_{partialOmega}=g x,y), end{array}displaystyle right.
Consider the following Neumann boundary value problem: left { textstylebegin{array}{l} Delta^{2} u t-1)+g(u t-1=h(t), quad tin[1,T]_{mathbf{Z}}, Delta u(0)=Delta u(T)=0, end{array}displaystyle right.
Consider the following second order three-point boundary value problem: left { textstylebegin{array}{l} -u t)=f u), quad tin[0,1], u(0)=0,qquad u(1)=frac{1}{2}u(frac{1}{2}), end{array}displaystyle right.
