We generalize Abrahamse’s interpolation theorem from the setting of a multiply connected domain to that of a more general Riemann surface. Our main result provides the scalar-valued interpolation theorem for the fixedpoint subalgebra of H∞ associated to the action of a Fuchsian group. We rely on two results from a paper of Forelli. This allows us to prove the interpolation result using duality ...

and Applied Analysis 3 In order to describe our main result, we need to define Λ0 ( 2 − q ( p − q‖a‖L∞ ) 2−q / p−2 ( p − 2 ( p − q)‖b ‖Lq∗ ) S p 2−q /2 p−2 q/2 p > 0, 1.3 where ‖a‖L∞ supx∈RNa x , ‖b ‖Lq∗ ∫ RN |b x |qdx 1/q∗ and Sp is the best Sobolev constant for the imbedding of H1 R into L R . Theorem 1.1. Assume that a1 , b1 b2 hold. If λ ∈ 0, q/2 Λ0 , Ea,λb admits at least two positive solu...

For a class of semilinear parabolic equations on a bounded domain Ω, we analyze the behavior of the solutions when the initial data varies in the phase space H 0 (Ω). We obtain both global solutions and finite time blow-up solutions. Our main tools are the comparison principle and variational methods. Particular attention is paid to initial data at high energy level; to this end, a basic new id...

Abstract A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this has sign-changing solution least energy. Moreover, show the energy level of strictly larger than double ground state solution.

Abstract We study a double phase Neumann problem with superlinear reaction which need not satisfy the Ambrosetti-Rabinowitz condition. Using Nehari manifold method, we show that has at least three nontrivial bounded ground state solutions, all sign information (positive, negative and nodal).

Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrödinger equations with attractive self-interaction. However, when selfinteraction becomes repulsive, it seems impossible to have bright solitary wave solution. Here we show that there exists symbiotic bright solitary wave solution of coupled nonlinear Schrödinger equations with repulsive self-interacti...

Abstract In this article, we use the Nehari manifold method to study a class of fourth-order even difference systems. First, show that there exist multiple periodic solutions non-autonomous system. Second, obtain sufficient conditions guarantee existence with prescribed minimal periods autonomous Our results generalize in reference.

In this paper, we discuss the existence and non-existence of weak solutions to non-linear problem with a fractional p-Laplacian introduced by ?-Hilfer operator, combining technique Nehari manifolds fibering maps. Also, obtain some results on operator manifold via Euler functional.