Sentence examples for problems of equation from inspiring English sources

To achieve these results, we are forced to require, similar as in [33], that τ Δ ( t ) ≥ τ 0 > 0, τ ∘ δ = δ ∘ τ, and τ ( [ t 0, ∞ ) T ) = [ τ ( t 0 ), ∞ ) T. It would be interesting to seek other methods for further study of oscillatory properties or asymptotic problems of equation (1.1) in the case where p ( t ) ≥ 1.

Many theorems and methods of nonlinear functional analysis have been applied to research the periodic problems of Equation (2), such as the upper and lower solutions method and monotone iterative technique [1 4], the continuation method of topological degree [5 7], variational method and critical point theory [8 10], the theory of the fixed point index in cones [11 16], etc.

Recently, Bereanu and Mawhin obtained several interesting results on the existence and multiplicity of the solutions for various boundary value problems of equation (1.4) by using the Leray-Schauder degree, the lower and upper solutions, and the method of variational calculation; see [8 15] and other related works; we can refer to [16 19].

The complicated mixed boundary problems of equations of heat conduction and elasticity are converted analytically into singular integral equations, which are solved numerically.

On the other hand, Equation 13 reformulates the problem of Equation 12.

The posedness of the Cauchy problem of equation (1.1) has been deeply investigated (see [2 14] etc).

Finally, v(R N,k) stands for eigenvectors of the problem of Equation 39.

For r = 2, the stability problem of Equation (1.4) has been proved by Rassias [16].

The dual problem of equation (16) can be obtained [31] as: (18).

The global weak solutions to the Cauchy problem of equation (1.2) have been studied extensively [17 22].

For r = 1, the stability problem of Equation (1.4) has been investigated by Cholewa [15].