Yazar "Sevim, E. Sengelen" seçeneğine göre listele

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    Bounded Solutions for Nonhomogeneous Double Phase Problems With Gradient Dependence
    (Wiley, 2026) Razani, A.; Sevim, E. Sengelen
    This paper investigates the existence of bounded weak solutions to a class of nonhomogeneous double phase problems involving -Laplacian and -Laplacian operators with solution-dependent weights. The problem is set on a bounded domain and features a nonlinear right-hand side that depends on both the solution and its gradient. We establish uniform bounds for the solution set through a Moser iteration technique and prove existence results using truncation methods and pseudomonotone operator theory. Our work extends previous results by considering more general weight structures and gradient-dependent nonlinearities under minimal regularity assumptions. The analysis combines Sobolev space theory, variational methods, and careful energy estimates to handle the interplay between the different growth conditions and degeneracies in the problem.
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    The dimension graph of a commutative ring
    (Taylor & Francis Inc, 2024) Babaei, S.; Sevim, E. Sengelen
    This paper introduces a simple graph associated to a commutative ring. Nonzero ideals I and J of a commutative ring R are called Krull dimension-dependent whenever dimR/(I+J)=min{dimR/I,dimR/J} . Based on this, we introduce the dimension graph of R. We study and investigate this graph, and we determine all rings with disconnected dimension graph. Moreover, we introduce strongly Krull dimension-dependent ideals, and we examine these ideals using a subgraph of the dimension graph.
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    The Krull dimension-dependent elements of a Noetherian commutative ring
    (World Scientific Publ Co Pte Ltd, 2024) Babaei, S.; Sevim, E. Sengelen
    In this paper, we introduce the Krull dimension-dependent elements of a Noetherian commutative ring. Let x, y be non-unit elements of a commutative ring R. x, y are called Krull dimension-dependent elements, whenever dim R/(Rx + Ry) = min{dim R/Rx, dim R/Ry}. We investigate the elements of a ring according to this property. Among the many results, we characterize the rings that all elements of them are Krull dimension-dependent and we call them, closed under the Krull dimension. Moreover, we determine the structure of the rings with Krull dimension at most 1. that are closed under the Krull dimension.