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1.
Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations
In this paper, we consider the problem of the existence of non-negative weak solution u of
having a given closed set S as its singular set. We prove that when
and S is a closed subset of Ω, then there are infinite many positive weak solutions with S as their singular set. Applying
this method to the conformal scalar curvature equation for n ≥ 9, we construct a weak solution
of
such that Sn is the singular set of u where L0 is the conformal Laplacian with respect to the standard metric of Sn. When n = 4 or 6, this kind of solution has been constructed by Pacard. 相似文献
2.
Wu Shaoping 《数学学报(英文版)》1991,7(1):4-12
LetL be a self-adjoint linear operator andN be the gradient of a functional ϕ, which is almost quadratic. We first give a theorem on the surjectivity of the operatorL+N, then apply the result to semilinear elliptic systems:
相似文献
3.
Shuang-jie Peng 《应用数学学报(英文版)》2006,22(1):137-162
Abstract Let Ω be the unit ball centered at the origin in
. We study the following problem
4.
Résumé Dans un célèbre papier ([3]), B. GIDAS et J.SPRUCK ont utilisé-sous des hypothèses adéquates- la technique du “blow up” pour
montrer que les solutionsu ∈C
0
∩C
1 (Ω) du problème
admettent une estimation a priori dansC
0
.
Dans ce travail, on montre que, si les solutionsu sont juste supposéesC
0
, une telle estimation a priori n’existe plus.
In a famous paper ([3]), B. GIDAS and J. SPRUCK used a “blow-up” argument to show that, under appropriate assumptions, all
the solutionsu ∈C
0
∩C
1 (Ω) of the problem
admit an a priori estimate inC
0
.
In this work, we show that, if one supposes the solutions are only inC
0
, such an a priori estimate does not hold. 相似文献
5.
The paper is devoted to the study of the behavior of the following mixed problem for large values of time:
6.
Francesco Leonetti 《Annali dell'Universita di Ferrara》1985,31(1):169-184
Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali
dei funzionali
sotto opportune ipotesi suA
ij
αβ
e sug.
Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA ij αβ andg.相似文献 7.
8.
J. Mossino 《Israel Journal of Mathematics》1978,30(1-2):14-50
This paper deals with some problems arising in plasma physics. The typical example is the following:
where
is the (neither local, nor monotone, nor continuous) operator:
. Using a quasi-variational approach, we prove the existence of minimal and maximal solutions for a weak form of this problem,
involving a multi-valued operator β. Various generalizations are treated.
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9.
The existence of a positive solution for the generalized predator-prey model for two species
|