Yazar "Ayazoglu R." seçeneğine göre listele

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  • Küçük Resim Yok
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    Existence and uniqueness of solutions of a nonlocal problem involving the p(x)-Laplacian
    (University of Craiova, 2014) Avci M.; Ayazoglu R.
    The object of this paper is to study a nonlocal problem involving the p(x)-Laplacian where nonlinearities f do not necessarily satisfy the classical conditions, such as Ambrosetti-Rabinowitz condition, but are limited by functions that do satisfy some specific conditions. By using the direct variational approach and the theory of the variable exponent Sobolev spaces, the existence and uniqueness of solutions is obtained.
  • Küçük Resim Yok
    Öğe
    On the boundedness of a B-Riesz potential in the generalized weighted B-Morrey spaces
    (Walter de Gruyter GmbH, 2016) Ayazoglu R.; Hasanov J.J.
    We consider the generalized shift operator associated with the Laplace-Bessel differential operator ? B = i=1 n 2 x i 2 +i=1 k ? i x ix i .$ \Delta -{B}=\sum -{i=1}^{n}\frac{\partial ^2 }{\partial x-i^2} +\sum -{i=1}^{k} \frac{\gamma -i }{x-i}\frac{\partial }{\partial x-i}. $ The maximal operator M ? ${M-{\gamma }}$ (B-maximal operator) and the Riesz potential I ?,? ${I-{\alpha ,\gamma }}$ (B-Riesz potential), associated with the generalized shift operator are investigated. We prove that the B-maximal operator M ? ${M-{\gamma }}$ and the B-singular integral operator are bounded from the generalized weighted B-Morrey space p,? 1 ,?,? (k,+ n )${{\cal M}-{p,\omega -1,\varphi ,\gamma }(\mathbb {R}-{k,+}^{n})}$ to p,? 2 ,?,? (k,+ n )${{\cal M}-{p,\omega -2,\varphi ,\gamma }(\mathbb {R}-{k,+}^{n})}$ for all 1