Infinitely many solutions for a class of stationary Schrödinger equations with non-standard growth

In this paper, we study the existence of infinitely many solutions for a class of stationary Schrödinger type equations in ?N involving the p(x)-Laplacian. The non-linearity is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition. The main arguments are based on the geometry supplied by Fountain Theorem. We also establish a Bartsch type compact embedding theorem for variable exponent spaces. © 2017 Informa UK Limited, trading as Taylor & Francis Group

Existence of one weak solution for p(X)-biharmonic equations involving a concave-convex nonlinearity

In the present paper, using variational approach and the theory of the variable exponent Lebesgue spaces, the existence of nontrivial weak solutions to a fourth order elliptic equation involving a p(x)-biharmonic operator and a concave-convex nonlinearity the Navier boundary conditions is obtained. © 2017, Drustvo Matematicara Srbije. All rights reserved

Multiple small solutions for p(x)-Schrödinger equations with local sublinear nonlinearities via genus theory

In this paper, we deal with the following p(x)-Schrödinger problem: (Formula Presented) where the nonlinearity is sublinear. We present the existence of infinitely many solutions for the problem. The main tool used here is a variational method and Krasnoselskii’s genus theory combined with the theory of variable exponent Sobolev spaces. We also establish a Bartsch-Wang type compact embedding theorem for the variable exponent spaces. © 2017, University of Szeged. All rights reserved

Multi-loop Model Reference Adaptive PID Control for Fault-Tolerance

This study demonstrates an application of multi-loop Model Reference Adaptive Control (MRAC) structure for enhancement of fault tolerance performance of closed-loop PID control systems. The presented multi-loop MRAC-PID control structure can be used to transform a conventional PID control system to an adaptive control system by combining an outer adaptation loop. This study shows that the proposed control structure can improve fault tolerance and fault detection performance of the existing closed-loop PID control systems without modifying any coefficients of PID controllers, and this asset is very useful for increasing robust control performance of the existing industrial control systems. This advantage originates from the reference input shaping technique that is implemented to combine adaptation and control loops. Numerical and experimental studies are presented to illustrate an application of the MRAC-PID control structure for rotor control applications

Multi-loop Model Reference Adaptive PID Control for Fault-Tolerance

This study demonstrates an application of multi-loop Model Reference Adaptive Control (MRAC) structure for enhancement of fault tolerance performance of closed-loop PID control systems. The presented multi-loop MRAC-PID control structure can be used to transform a conventional PID control system to an adaptive control system by combining an outer adaptation loop. This study shows that the proposed control structure can improve fault tolerance and fault detection performance of the existing closed-loop PID control systems without modifying any coefficients of PID controllers, and this asset is very useful for increasing robust control performance of the existing industrial control systems. This advantage originates from the reference input shaping technique that is implemented to combine adaptation and control loops. Numerical and experimental studies are presented to illustrate an application of the MRAC-PID control structure for rotor control applications