In this paper, we study the existence of least-energy nodal (sign-changing) weak solutions for a class fractional Orlicz equations given by ( − △ g ) α u + = K x f , in R N where ⩾ 3 is g-Laplace operator, while ∈ C 1 and positive continuous function. Under suitable conditions on K, prove compact embeddings result weighted Orlicz–Sobolev spaces. Next, minimization argument Nehari manifold quant...

In this thesis we study operators, and spaces of operators on a Hubert space defined by intertwining relations. The classical Hankel operators are those operators which intertwine the unilateral shift and its adjoint. We consider generalised Hankel operators relative to shifts and relative to families of shifts and give generalisations of the classical theorems of Nehari and Hartman. In contras...

We extend to the case of many competing densities the results of the paper [7]. More precisely, we are concerned with an optimal partition problem in N -dimensional domains related to the method of nonlinear eigenvalues introduced by Z. Nehari, [16]. We prove existence of the minimal partition and some extremality conditions. Moreover, in the case of two–dimensional domains we give an asymptoti...

where r(x) >0 and p(x) are both continuous on [a, oo) and p(x) does not change sign, and related conjugate point properties to oscillation. They gave extensive evidence indicating that the oscillatory behavior when p(x) is positive is essentially different from that when p(x) is negative. Relatively little is known in general when p(x) changes sign or when derivative terms of order less than fo...

The Disturbance observer (DOB) method is known to be effective in enhancing the performance of dynamic systems in the presence of disturbances. DOBs of various structures have been proposed to improve systems’ sensitivity functions for better disturbance rejection performance and robustness. However, the improvement to the sensitivity function may deteriorate robustness and transient responses....

This note deals with performance bounds for the -optimal control of discrete-time LTI plants. The case studied corresponds to stable scalar plants with arbitrary relative degree but no finite non-minimum phase zero. By using Nehari’s Theorem and a reformulation of the standard Youla Parameterization a closed-form expression for the characteristic polynomial of the associated eigenvalue problem ...

We investigate the number of times that nontrivial solutions of equations u′′ + p(z)u = 0 in the unit disk can vanish—or, equivalently, the number of times that solutions of S(f) = 2p(z) can attain their values—given a restriction |p(z)| ≤ b(|z|). We establish a bound for that number when b satisfies a Nehari-type condition, identify perturbations of the condition that allow the number to be in...