• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.701-716
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• 2021

In this present article, we construct a new framework that's we call the weighted geometric realization of 2 and 3-simplexes. On this new weighted framework, we construct a nonself-adjoint 2-simplex Laplacian L and a self-adjoint 2-simplex Laplacian N. We propose general conditions to ensure sectoriality for our new nonself-adjoint 2-simplex Laplacian L. We show the relation between the essential spectra of L and N. Finally, we prove the absence of the essential spectrum for our 2-simplex Laplacians L and N.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.21-36
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• 2024

In this paper, we study the existence of solutions for hybrid fractional differential equations with p-Laplacian operator involving fractional Caputo derivative of arbitrary order. This work can be seen as an extension of earlier research conducted on hybrid differential equations. Notably, the extension encompasses both the fractional aspect and the inclusion of the p-Laplacian operator. We build our analysis on a hybrid fixed point theorem originally established by Dhage. In addition, an example is provided to demonstrate the effectiveness of the main results.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.725-737
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• 2024

This article introduces the concepts of Energy and Laplacian Energy (LE) of Domination in Hesitancy fuzzy graph (DHFG). Also, the adjacency matrix of a DHFG is defined and proposed the definition of the energy of domination in hesitancy fuzzy graph, and Laplacian energy of domination in hesitancy fuzzy graph is given.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.723-738
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• 2015

In this paper, the prescribed mean curvature Rayleigh p-Laplacian equation with a deviating argument

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.15-23
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• 2001

This paper gives the sufficient conditions for the existence of positive solution of a quasilinear elliptic with homogeneous Dirichlet boundary conditon.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.33-44
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• 1998

This paper is concerned with the existence of mutiple positive solution of (equation omitted) with Dirichlet boundary condition.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.5
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• pp.1761-1777
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• 2021

An image with infrared features and visible details is obtained by processing infrared and visible images. In this paper, a fusion method based on Laplacian pyramid and generative adversarial network is proposed to obtain high quality fusion images, termed as Laplacian-GAN. Firstly, the base and detail layers are obtained by decomposing the source images. Secondly, we utilize the Laplacian pyramid-based method to fuse these base layers to obtain more information of the base layer. Thirdly, the detail part is fused by a generative adversarial network. In addition, generative adversarial network avoids the manual design complicated fusion rules. Finally, the fused base layer and fused detail layer are reconstructed to obtain the fused image. Experimental results demonstrate that the proposed method can obtain state-of-the-art fusion performance in both visual quality and objective assessment. In terms of visual observation, the fusion image obtained by Laplacian-GAN algorithm in this paper is clearer in detail. At the same time, in the six metrics of MI, AG, EI, MS_SSIM, Q_abf and SCD, the algorithm presented in this paper has improved by 0.62%, 7.10%, 14.53%, 12.18%, 34.33% and 12.23%, respectively, compared with the best of the other three algorithms.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.393-402
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• 2006

We investigate relations between multiplicity of solutions and source terms in a elliptic equation. We have a concerne with a sharp result for multiplicity of a nonlinear Laplacian differential equation.

• East Asian mathematical journal
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• v.34 no.5
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• pp.577-585
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• 2018

For the purpose of characterizing subharmonic or ${\mathcal{M}}$-subharmonic Hardy classes in the unit ball of ${\mathbb{C}}^n$, we establish fundamental identities between integral means in terms of volume integrals and Green's functions.