Sentence examples for a general existence from inspiring English sources

(II) In 1998, Park and Kum [17] applied Proposition 5.1 with A = B to a general existence theorem on a generalized variational inequalities and some of its consequences.

In Section 3, a general existence result is presented for (1.1) and (1.2).

Now we prove a general existence principle for singular boundary value problem (1.1).

The approach is based on a general existence criterion for chaotic dynamics of n-dimensional maps and inequality techniques.

Then, by using cone theoretic techniques, a general existence theorem for (1.4) was obtained when f ( t, x ) satisfies some growth conditions.

Mainly, via the topological degree theory, a general existence theorem is proved, which provides an effective method in the qualitative theory for nonlinear dynamic equations on time scales.

This approach to impulsive differential equations also used the critical point theory for the existence of solutions of a nonlinear Dirichlet impulsive problem and in [19] some new comparison principles and the monotone iterative technique to establish a more general existence theorem for a periodic boundary value problem.

In this section we give a more general existence result than Theorem 3.11 by assuming the existence of -lower and upper solutions.

A new and general existence and uniqueness theorem of almost automorphic solutions to the equation is established.

A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equation, in complex Banach spaces, with Stepanov-like almost automorphic coefficients.

A new and general existence and uniqueness theorem of almost automorphic solutions for the semilinear fractional differential equation (1). in complex Banach spaces, with Stepanov-like almost automorphic coefficients is obtained, and applications to fractional relaxation-oscillation equations are presented.