The boundary value condition of holds, a c 1 - b φ q ( 0 ) ( c 2 ) = 0, c c 1 + d c 2 = 0. Since (ad + bc) > 0, we have c 1 = 0, c 2 = 0, which together with hypothesis (20), implies that (0, 0)∈ Ω.
Note that the inclusion (chiin H(Omega)) assumes that the following homogeneous boundary-value conditions hold: w=0, qquadpsi=W= 0,0) quad mbox{on } gamma_{0}.
A function is said to be a position of the BVP (1.1) if satisfies the following: for and satisfies boundary value conditions (1.1); hold for.
Then, there exists a unique matrix solution Q n ( k ) ( r ) = q n i j ( k ) ( r ) of Equation 12 such that relation (21) holds, and boundary value condition (22) is satisfied.
Thus, from the boundary value condition (x_{1}(0)=0), one has that (3.4) holds.
By Lemma 2.2, D 0 + α x ( t ) = 0 has solution x ( t ) = c 0 + c 1 t + c 2 t 2, c 0, c 1, c 2 ∈ ℝ. Combining with the boundary value condition of BVP (1.1), one has (3.1) hold.
with boundary value condition (k).
By boundary value condition, we have (2.12).
This paper deals with the existence of solutions of (1 - 3) with periodic-like boundary value condition, Neumann boundary value condition, or Dirichlet boundary value condition, respectively.
