• Title, Summary, Keyword: p-Laplacian

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POSITIVE SOLUTIONS TO A FOUR-POINT BOUNDARY VALUE PROBLEM OF HIGHER-ORDER DIFFERENTIAL EQUATION WITH A P-LAPLACIAN

  • Pang, Huihui;Lian, Hairong;Ge, Weigao
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.59-74
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    • 2010
  • In this paper, we obtain the existence of positive solutions for a quasi-linear four-point boundary value problem of higher-order differential equation. By using the fixed point index theorem and imposing some conditions on f, the existence of positive solutions to a higher-order four-point boundary value problem with a p-Laplacian is obtained.

ON PERIODIC BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR FUNCTIONAL DIFFERENCE EQUATIONS WITH p-LAPLACIAN

  • Liu, Yuji;Liu, Xingyuan
    • Communications of the Korean Mathematical Society
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    • v.24 no.1
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    • pp.29-40
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    • 2009
  • Motivated by [Linear Algebra and its Appl. 420(2007), 218-227] and [Linear Algebra and its Appl. 425(2007), 171-183], we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional difference equations with p-Laplacian. Sufficient conditions for the existence of at least one solution of this problem are established.

THE NEHARI MANIFOLD APPROACH FOR DIRICHLET PROBLEM INVOLVING THE p(x)-LAPLACIAN EQUATION

  • Mashiyev, Rabil A.;Ogras, Sezai;Yucedag, Zehra;Avci, Mustafa
    • Journal of the Korean Mathematical Society
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    • v.47 no.4
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    • pp.845-860
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    • 2010
  • In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.

THE SPECTRAL GEOMETRY OF EINSTEIN MANIFOLDS WITH BOUNDARY

  • Park, Jeong-Hyeong
    • Journal of the Korean Mathematical Society
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    • v.41 no.5
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    • pp.875-882
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    • 2004
  • Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\Delta$$_{p}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\Delta$$_{p}$,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.ant.

INFINITELY MANY SMALL SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL SOBOLEV AND HARDY EXPONENTS

  • Liang, Sihua;Zhang, Jihui;Fan, Fan
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1143-1156
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    • 2010
  • In this paper, we study the following p&q-Laplacian problem with critical Sobolev and Hardy exponents {$-{\Delta}_pu-{\Delta}_qu={\mu}\frac{{\mid}u{\mid}^{p^*(s)-2}u}{{\mid}x{\mid}^s}+{\lambda}f(x,\;u)$, in $\Omega$, u=0, on $\Omega$, where ${\Omega}\;{\subset}\;\mathbb{R}^{\mathbb{N}}$ is a bounded domain and ${\Delta}_ru=div({\mid}{\nabla}u{\mid}^{r-2}{\nabla}u)$ is the r-Laplacian of u. By using the variational method and concentration-compactness principle, we obtain the existence of infinitely many small solutions for above problem which are the complement of previously known results.

SOME RESULTS OF EVOLUTION OF THE FIRST EIGENVALUE OF WEIGHTED p-LAPLACIAN ALONG THE EXTENDED RICCI FLOW

  • Azami, Shahroud
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.953-966
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    • 2020
  • In this article we study the evolution and monotonicity of the first non-zero eigenvalue of weighted p-Laplacian operator which it acting on the space of functions on closed oriented Riemannian n-manifolds along the extended Ricci flow and normalized extended Ricci flow. We show that the first eigenvalue of weighted p-Laplacian operator diverges as t approaches to maximal existence time. Also, we obtain evolution formulas of the first eigenvalue of weighted p-Laplacian operator along the normalized extended Ricci flow and using it we find some monotone quantities along the normalized extended Ricci flow under the certain geometric conditions.

INFINITELY MANY SOLUTIONS FOR (p(x), q(x))-LAPLACIAN-LIKE SYSTEMS

  • Heidari, Samira;Razani, Abdolrahman
    • 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.