A state observer design procedure is proposed for nonlinear locally Lipschitz systems with high relative degree from the available for measurements output to the nonlinearity. The possible presence of disturbances is taken into account. The solution is based on logic-based control and the high order supertwisting observer. The approach is applicable to nonlinear systems with bounded solutions. ...

In this paper, we deal with a class of semilinear elliptic equation in a bounded domain Ω ⊂ R , N ≥ 3, with C boundary. Using a new fixed point result of the Krasnoselskii’s type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.

It is proved that the stochastic porous media equation in a bounded domain of R, with multiplicative noise, with a monotone nonlinearity of polynomial growth has a unique nonnegative solution in H−1 (in particular is nonnegative measure-valued), provided the initial data is in H−1 and nonnegative. AMS subject Classification 2000: 76S05, 60H15.

We consider quasilinear parabolic nondiagonal systems of equations with additional terms quadratic nonlinearity in the gradient. study local continuity solutions that are not necessarily bounded under optimal smoothness conditions on principal matrix and one-sided strongly nonlinear terms.

The Immersion and Invariance (I&I) wind speed estimator is a powerful widely-used technique to estimate the rotor effective on horizontal axis turbines. Anyway, its global convergence proof rather cumbersome, which hinders extension of method time-delayed and/or uncertain systems. In this letter, we illustrate that circle criterion can be used as an alternative prove I\&I estimator. This also o...

In this paper, we deal with the semilinear wave equation with strong damping. By choosing a suitable state space, we characterize the interpolation and extrapolation spaces of the operator matrix Aθ, analysis the criticality of the ε-regular nonlinearity with critical growth. Finally, we investigate the global existence of the ε-regular solutions which have bounded X ×X norms on their existence...

Using variational methods we study the generalization of two classical second order periodic problems in the context of time scales. On the one hand, we study a forced pendulum-type equation. On the other hand, we obtain solutions for a bounded nonlinearity under Landesman–Lazer type conditions. AMS subject classification: 39A12, 39A99.

In this paper, we consider the controllability of a semilinear heat equation with a nonlinearity that has a superlinear growth at infinity with Dirichlet boundary conditions in a bounded domain of RN . The proof of the main result in this paper involve such inequalities and rely on the study of these linear problems and appropriate fixed point arguments.