Sentence examples for boundary value condition the from inspiring English sources

Among them, as a classical non-resonance boundary value condition, the integer order Sturm-Liouville BVPs have been studied for a long time.

Under the integrable boundary value condition, the existence and uniqueness of the solutions of this equation are discussed by using new Riesz representations of linear maps and the Schrödinger fixed point theorem.

On the other hand, different from that in the case of the Dirichlet boundary value condition, the standard regularized problem of problem (1.1 - 1.3 1.1 - 1.3ell posed, and thus a modisied regularized problem for (1.1)-(1.3) is conotdered.

Under periodic-integrable boundary value condition, the existence of the solutions of this equation is discussed by the method of the operator theory and the Schauder fixed point theorem.

With appropriate boundary value conditions, the existence of positive solution of equation (2) is significant and helpful.

And for the restrictions of the boundary value conditions, the above-mentioned operator Φ in (1.3), which is suitable for the entire space, is inappropriate in this paper.

The most significant feature of the paper is that the definition of the homogeneous boundary value condition of the above equation is given.

Theorem 3.2 Let u be the unique nonnegative bounded solution of (1.1) with the homogeneous boundary value condition in the sense of Definition  3.1.

In other words, since the equation is nonlinear, how to quote a suitable boundary value condition matching the equation seems very difficult.

Using Kruzkov's bi-variables method, by choosing a suitable test function, the stability of the entropy solutions is proved based on the partial boundary value condition, provided that the convection term has the degeneracy on the boundary.

We only give some ideas of how to give the partial boundary value condition to assure the posedness of the weak solutions.