具Hardy-Sobolev临界指数的奇异椭圆方程多解的存在性

运用变分方法研究了下面问题-Δpu=μupx(s)s-2u f(x,u),x∈Ω,u=0,x∈Ω,多重解的存在性,其中Ω是一个具有光滑边界的有界区域.     

Existence, Multiplicity and Infinite Solvability of Positive Solutions for One-Dimensional p-Laplacian

The existence, multiplicity and infinite solvability of positive solutions are established for some two-point boundary value problems of one-dimensional p-Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number.     

具p-Laplacian算子型奇异边值问题的正解

考虑一类p-Laplacian算子型泛函微分方程的奇异边值问题,利用锥不动点定理,得到了其正解及多个正解存在的充分条件．     

Multiple positive solutions for one-dimensional p-Laplacian boundary value problems

By means of the Leggett-Williams fixed-point theorem, criteria are developed for the existence of at least three positive solutions to the one-dimensional p-Laplacian boundary value problem, ((y′))′ + g(t)f(t,y) = 0, y(0) - B₀(y′(0)) = 0, y(1) + B₁(y′(1)) = 0, where (v) |v|^p−2v, p > 1.     

VISCOSITY SOLUTION THEORY OF A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS Ⅰ. UNIQUENESS AND EXISTENCE OF VISCOSITY SOLUTIONS

ThisresearchissupportedbytheNationalNaturalSciencesFoundationofChina.1.IntroductionInthispaper,weseektoestablishthecomparisonprinciple,regularity,ekistenceandsomegeometricpropertiesoftheinterfaceoftheviscositysolutionsforthefollowingfullynonlineardegenerateequations(Problem(C)):withFsatisfyingthefollowingassumptions:Fisdegenerateparabolic,i.e.F(q,X Y)5F(q,X),VY20,whereSadenotesthespaceofnxnsymmetricmatriceswiththeusualordering.wherellXlll~ItrX l ltrX--l,X~X X--,X 20,X--50,A,B20,p>2…     

POSITIVE SOLUTION FOR NONLINEAR SINGULAR BOUNDARY VALUE PROBLEMS

Under suitable conditions on f(·,u), it is shown that the two-point boundaryvalue problem((u'))' + λq(t)f(u) = 0in (0, 1),u(0) = u(1) = 0,has two positive solution or at least one positive solution for λ in a compatibleinterval.     

具多偏差变元的n-维p-Laplacian方程周期解的存在性

研究了一类具多偏差变元的n-维p-Laplacian方程周期解的存在性,利用迭合度理论得到了存在周期解的新条件.     

Multiplicity of Solutions of the Weighted p-Laplacian with Isolated Singularity and Diffusion Suppressed by Convection

In this paper, the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and di?usion suppressed by convection ?div(|x|^α|?u|^p?2?u) + λ 1/|x|^β |?u|^p?2?u · x = |x|^γg(|x|) in B \ {0} subject to nonlinear Robin boundary value condition |x|^α|?u|^p?2?u · ?n = A ? ρu on ?B,where λ > 0, B ? R^N(N ≥ 2) is the unit ball centered at the origin, α > 0, p > 1, β ∈ R, γ > ?N, g ∈ C([0,1]) with g(0) > 0, A ∈ R, ρ > 0 and ?n is the unit outward normal. The same problem with di?usion promoted by convection, namely λ ≤ 0, has already been discussed by the last two authors (Song-Yin (2012)), where the existence, nonexistence and classi?cation of singularities for solutions are presented. Completely di?erent from [Song, H. J. and Yin, J. X., Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection, Math. Meth. Appl. Sci., 35, 2012, 1089–1100], in the present case λ > 0, namely the di?usion is suppressed by the convection, non-singular solutions are not only existent but also may be in?nite which vary according only to the values of solutions at the isolated singular point. At the same time, the singular solutions may exist only if the di?usion dominates the convection.     

Two nontrivial solutions for quasilinear periodic equations

In this paper we study a nonlinear periodic problem driven by the ordinary scalar p-Laplacian and with a Carathéodory nonlinearity. We establish the existence of at least two nontrivial solutions. Our approach is variational based on the smooth critical point theory and using the ``Second Deformation Theorem".

     

具ρ-aplacian算子非齐次辊舍型二阶微分方程多点边值问题(英文)

A class of multi-point boundary value problems are studied.Easily verified suffcient conditions to guarantee the existence of at least one solutions of above mentioned BVPs are established.The examples are presented to illustrate the main results.