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Existence and Multiplicity Results for a degenerate elliptic equation

Acta Mathematica Sinica,English Series 2006年第3期22卷 665-670页

作者： Wei DONG Jian Tao CHEN Hebei University of Engineering

The goal of this paper is to study the multiplicity result of positive solutions of a class of degenerate elliptic equations. On the basis of the mountain pass theorems and the sub- and supersolutions argument for p-Laplacian operators, under suitable conditions on the nonlinearity f（x, s）, we show the following problem：-△pu=λu^α-a（x）u^q in Ω,u│δΩ=0 possesses at least two positive solutions for large λ, where Ω is a bounded open subset of R^N, N ≥ 2, with C^2 boundary, λ is a positive parameter, Ap is the p-Laplacian operator with p 〉 1, α, q are given constants such that p - 1 〈α 〈 q, and a（x） is a continuous positive function in Ω^-.

关键词： degenerate elliptic equation mountain pass theorem maximal positive solution

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THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR degenerate elliptic equationS

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Acta Mathematica Scientia 2005年第4期25卷 577-586页

作者：赵俊宁曾小明 Department of Mathematics Xiamen University Xiamen 361005 China

In this paper, the first boundary value problem for quasilinear equation of the form △A（u,x）＋∑i=1^m δb^i（u,x）/δxi＋c（u,x）=0,Au（u,x） ≥0is studied. By using the compensated compactness theory, some results on the existence of weak solution are established. In addition, under certain condition the uniqueness of solution is proved.

关键词： Dirichlet problem degenerate elliptic equation existence of solutions

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SHOCK DIFFRACTION PROBLEM BY CONVEX CORNERED WEDGES FOR ISOTHERMAL GAS

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Acta Mathematica Scientia 2021年第4期41卷 1130-1140页

作者： Qin WANG Kyungwoo SONG Department of Mathematics Yunnan UniversityKunming 650091China Department of Mathematics Kyung Hee UniversitySeoul 02447Korea

We are concerned with the shock diffraction configuration for isothermal gas modeled by the conservation laws of nonlinear wave *** reformulate the shock diffraction problem into a linear degenerate elliptic equation in a fixed bounded *** degeneracy is of Keldysh typw-the derivative of a solution blows up at the *** establish the global existence of solutions and prove the C0,1/2-regularity of solutions near the degenerate *** also compare the difference of solutions between the isothermal gas and the poly tropic gas.

关键词： Nonlinear wave system isothermal gas shock diffraction degenerate elliptic equation Riemann problem regularity

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Configurations of Shock Regular Reflection by Straight Wedges

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Communications on Applied Mathematics and Computation 2023年第3期5卷 1256-1273页

作者： Qin Wang Junhe Zhou Department of Mathematics and Statistics Yunnan UniversityKunming 650091YunnanChina

We are concerned with the shock regular reflection configurations of unsteady global solutions for a plane shock hitting a symmetric straight *** has been known that patterns of the shock reflection are various and complicated,including the regular and the Mach *** of the fundamental issues for the shock reflection have not been ***,there are great progress on the mathematical theory of the shock regular reflection problem,especially for the global existence,uniqueness,and structural stability of *** this paper,we show that there are two more possible configurations of the shock regular reflection besides known four *** also give a brief proof of the global existence of solutions.

关键词： Shock regular reflection Transonic shock Prandtl-Meyer reflection degenerate elliptic equation Two-dimensional Euler equations

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