Sentence examples for problems were established from inspiring English sources

Later, optimality and duality results for PDI&PDE-constrained optimization problems were established by Pitea et al. in [14] and [15].

Since then, optimality conditions of Fritz John and Karush-Kuhn-Tucker type for differentiable or nondifferentiable nonconvex multiobjective programming problems were established under different assumptions.

For example, optimality conditions of Fritz-John and Karush-Kuhn-Tucker type for nondifferentiable convex multiobjective programming problems were established by Kanniappan.

For the absorption case ( u p is replaced by − u p in (1.1)) and the supercritical case ( p > 1 + 2 N in (1.1)), some similar results about the asymptotic behavior of solutions for these problems were established by a lot of papers, see [18 20].

However, with respect to symmetric solutions for nonlinear elliptic systems, we remark that several symmetric results for singular problems were established in [24 26] and when (G=O(mathbb{N})), a handful of radial and nonradial results for nonsingular problems were obtained in [27].

A number of comprehension problems were established and relevant questions were revised accordingly.

The uniform separability of these problems is established.

Strong convergence theorems for common solutions of the problems are established in infinite dimension Hilbert spaces.

The relationships between the variational-like inequalities and the nondifferentiable pseudoinvex optimization problems are established.

Stability, almost coercive stability, and coercive inequalities for the solutions of difference problems are established.

A posteriori error estimates of finite-element solutions for those problems are established in Section 3.