In this paper, we study the following first-order nonperiodic Hamiltonian system ż = JHz(t, z), where H ∈ C1(R× R ,R) is the form H(t, z) = 1 2 L(t)z · z + R(t, z). Under weak superquadratic condition on the nonlinearitiy. By applying the generalized Nehari manifold method developed recently by Szulkin and Weth, we prove the existence of homoclinic orbits, which are ground state solutions for a...

In this paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary condition and sign-changing potential. With the help of the Nehari manifold, we prove that the semilinear elliptic equation: −∆u+ u = λf(x)|u|q−2u in Ω, ∂u ∂ν = g(x)|u|p−2u on ∂Ω, has at least two nontrivial nonnegative solutions for λ is sufficiently small.

Abstract In this paper, we study the existence of non-negative non-trivial solutions for a class double-phase problems where source term is Caratheodory function that satisfies Ambrosetti–Rabinowitz type condition in framework Sobolev–Orlicz spaces with variable exponents complete manifold. Our approach based on Nehari manifold and some variational techniques. Furthermore, Hölder ine-quality, c...

Received 13 June 2008; Revised 12 October 2008; Accepted 20 November 2008 Recommended by Stevo Stevic This paper shows that if S is a bounded linear operator acting on the weighted Bergman spaces Aα on the unit ball in C n such that STzi TziS i 1, . . . , n , where Tzi zif and Tzi P zif ; and where P is the weighted Bergman projection, then S must be a Hankel operator. Copyright q 2008 Y. Lu an...

A Kirchhoff equation type with memory term competing a logarithmic source is considered. By using potential well theory, we obtained the global existence of solution for initial data in stability set created from Nehari Manifold and prove blow up results instability set.

We study here a particular application of the theory of Hankel operators to robust control. The techniques of superoptimal Nehari extension developed by Young [16] are employed to derive some properties of a particular controller of a rational function G, called superoptimally robust stabilizing controller. Using this controller, we generalize to the multivariable case some results which appear...

This note presents a frequency domain method to solve the standard control problem for processes with a single delay. For a given bound on the closed-loop norm, there exist proper stabilizing controllers that achieve this bound if and only if both the corresponding delay-free problem and an extended Nehari problem with a delay (or a one-block problem) are all solvable. The solvability of the ex...

We formulate a minimax game which is equivalent to the Nehari problem in the sense that this minimax game is well-posed if and only if the Hankel norm of a given operator is less than a prescribed constant. This game and the dual game provide us with physical interpretations of the Riccati operators that are commonly used in the solution of the Nehari problem.