Nonlinear Partial Differential Equations

In the paper we find conditions on the pair $(\omega _1,\omega _2)$ which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space $\mathcal {M}_{p,\omega _1}$ to another $\mathcal {M}_{p,\omega _2}$, $1<p<\infty $, and from the space $\mathc…

We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave e…

• HÜSNÜ ATA ERBAY

We continue our previous study of improved Hardy, Rellich and uncertainty principle inequalities on a Riemannian manifold M M , started in our earlier paper from 2009. In the present paper we prove new weighted Hardy-Poincaré, Rellich type inequalities as well as an improved version of our uncertainty principle inequa…

• İSMAİL KÖMBE

A magnetic field is defined by the property that its divergence is zero in a three-dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to study the magnetic flow associated wit…

• İSMAİL GÖK

A magnetic field is defined by the property that its divergence is zero in a three-dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to study the magnetic flow associated wit…

• ZEHRA ÖZDEMİR

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• İREM KÜPELİ ERKEN

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• CENGİZHAN MURATHAN

In this paper, by using variational approach and Krasnoselskii's genus theory, we show the existence and multiplicity of the solutions of the p(x)-Kirchhoff type equation. Copyright © 2011 John Wiley & Sons, Ltd.

• BİLAL ÇEKİÇ

We define weighted variable Sobolev capacity and discuss properties of capacity in the space 𝑊 1 , 𝑝 ( ⋅ ) ( ℝ 𝑛 , 𝑤 ) . We investigate the role of capacity in the pointwise definition of functions in this space if the Hardy-Littlewood maximal operator is bounded on the space 𝑊 1 , 𝑝 ( ⋅ ) ( ℝ 𝑛 , 𝑤 ) . Also it is sho…

Abstract In this article, for a time-fractional diffusion-wave equation ∂ t α u ( x , t ) = − A u ( x , t ) , 0 < t < T with fractional order α ∈ (1, 2), we consider the backward problem in time: determine u (⋅, t ), 0 < t < T by u (⋅, T ) and ∂ t u (⋅, T ). We prove that there exists a countably infinite set Λ ⊂ (0,…

• MASAHİRO YAMAMOTO

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• FATİH DERİNGÖZ

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