• 제목/요약/키워드: p-Laplacian systems

검색결과 11건 처리시간 0.03초

THREE SOLUTIONS TO A CLASS OF NEUMANN DOUBLY EIGENVALUE ELLIPTIC SYSTEMS DRIVEN BY A (p1,...,pn)-LAPLACIAN

  • Afrouzi, Ghasem A.;Heidarkhani, Shapour;O'Regan, Donal
    • 대한수학회보
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    • 제47권6호
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    • pp.1235-1250
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    • 2010
  • In this paper we establish the existence of at least three weak solutions for Neumann doubly eigenvalue elliptic systems driven by a ($p_1,\ldots,p_n$)-Laplacian. Our main tool is a recent three critical points theorem of B. Ricceri.

FUNDAMENTAL THEOREM OF UPPER AND LOWER SOLUTIONS FOR A CLASS OF SINGULAR (p1, p2)-LAPLACIAN SYSTEMS

  • XU, XIANGHUI;LEE, YONG-HOON
    • East Asian mathematical journal
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    • 제31권5호
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    • pp.727-735
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    • 2015
  • We introduce the fundamental theorem of upper and lower solutions for a class of singular ($p_1,\;p_2$)-Laplacian systems and give the proof by using the Schauder fixed point theorem. It will play an important role to study the existence of solutions.

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

  • Heidari, Samira;Razani, Abdolrahman
    • 대한수학회논문집
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    • 제36권1호
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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.

BOUNDARY VALUE PROBLEMS FOR NONLINEAR PERTURBATIONS OF VECTOR P-LAPLACIAN-LIKE OPERATORS

  • Manasevich, Raul;Mawhin, Jean
    • 대한수학회지
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    • 제37권5호
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    • pp.665-685
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    • 2000
  • The aim of this paper is to obtain nonlinear operators in suitable spaces whise fixed point coincide with the solutions of the nonlinear boundary value problems ($\Phi$($\upsilon$'))'=f(t, u, u'), l(u, u') = 0, where l(u, u')=0 denotes the Dirichlet, Neumann or periodic boundary conditions on [0, T], $\Phi$: N N is a suitable monotone monotone homemorphism and f:[0, T] N N is a Caratheodory function. The special case where $\Phi$(u) is the vector p-Laplacian $\mid$u$\mid$p-2u with p>1, is considered, and the applications deal with asymptotically positive homeogeneous nonlinearities and the Dirichlet problem for generalized Lienard systems.

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EXISTENCE OF POSITIVE SOLUTIONS FOR BVPS TO INFINITE DIFFERENCE EQUATIONS WITH ONE-DIMENSIONAL p-LAPLACIAN

  • Liu, Yuji
    • 충청수학회지
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    • 제24권4호
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    • pp.639-663
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    • 2011
  • Motivated by Agarwal and O'Regan ( Boundary value problems for general discrete systems on infinite intervals, Comput. Math. Appl. 33(1997)85-99), this article deals with the discrete type BVP of the infinite difference equations. The sufficient conditions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main results. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multi-fixed-point theorems can be extended to treat BVPs for infinite difference equations. The strong Caratheodory (S-Caratheodory) function is defined in this paper.

SUFFICIENT CONDITIONS FOR THE INTERSECTION PROPERTY IN GENERALIZED LI$\acute{E}$NARD SYSTEMS

  • Kim, Yong-In
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제18권3호
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    • pp.245-253
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    • 2011
  • Some new results on the intersection property of all nonzero solutions of a class of planar systems of Li$\acute{e}$nard type with vertical isoclines are obtained. The results of this paper generalize some previous results on this field.