We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation $ \begin{equation*} u_{t} = \Delta u + |u|^{p} \end{equation*} $ on complete Riemannian manifolds dimension n \geq 5 with nonnegative Ricci tensor, when p is smaller than critical Sobolev exponent \frac{n+2}{n-2} $.

Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for constructing the best approximation to a reference point from the set of Kuhn-Tucker points of a general Hilbertian composite monotone inclusion problem. Applications...

We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in ...

We propose a stochastic Forward Douglas-Rachford Splitting framework for finding a zero point of the sum of three maximally monotone operators in real separable Hilbert space, where one of them is cocoercive. We first prove the weak almost sure convergence of the proposed method. We then characterize the rate of convergence in expectation in the case of strongly monotone operators. Finally, we ...

This paper proposes an iterative method for solving strongly monotone equilibrium problems by using gap functions combined with double projection-type mappings. Global convergence of the proposed algorithm is proved and its complexity is estimated. This algorithm is then coupled with the proximal point method to generate a new algorithm for solving monotone equilibrium problems. A class of line...

The fundamental property of strongly monotone systems, and strongly cooperative systems in particular, is the limit set dichotomy due to Hirsch: if x(0) < y(0), then either ω(x) < ω(y), or ω(x) = ω(y) and both sets consist of equilibria. We provide here a counterexample showing that this property need not hold for (non-strongly) cooperative systems.

The two-dimensional systems of first order nonlinear differential equations (S1) x? = p(t)y?, y? q(t)x? and (S2) + p(t)y? 0, 0 are analyzed using the theory rapid variation. This approach allows us to prove that all strongly increasing solutions system (and, respectively, decreasing ) rapidly varying functions under assumption p q varying. Also, asymptotic equivalence relations for these given.

For strongly monotone dynamical systems, the dynamics alternative for smooth discrete-time systems turns out to be a perfect analogy of celebrated Hirsch's limit-set dichotomy continuous-time semiflows. In this paper, we first present sharpened C 1 -smooth dissipative system { F 0 n } ∈ N (with an attractor A ), which concludes that there is positive integer m such any orbit either manifestly u...