A NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF NON NEGATIVE SOLUTIONS FOR SOME SEMILINEAR NON MONOTONE EQUATIONS

被引：129

作者：

BARAS, P ^{[1
]}

PIERRE, M ^{[1
]}

机构：

[1] UER MATH,F-54506 VANDOEUVRE NANCY,FRANCE

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 1985年 / 2卷 / 03期

关键词：

D O I：

10.1016/S0294-1449(16)30402-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a necessary and sufficient condition on f∈Lloc1(U), f ≥ 0 for the existence of a nonnegative solution for the equation u(x)=∫UN(x,y)j(u(y))dy+f(x)a.e.x∈U. Here j is a convex function from [0, ∞[into [0, ∞[and N is a nonnegative kernel of Lloc1(U×U). This equation contains as a special case elliptic and parabolic semilinear equations of nonmonotone type like, for instance {−Δu=uΓ+gonΩ,g≥0andΓ>1givenu≥0u=0on∂Ω and its parabolic version. These examples are treated in detail. Necessary conditions in terms of W2,Γ″-capacity are also given. © 2016 L'Association Publications de l'Institut Henri Poincaré

引用

页码：185 / 212

页数：28

共 12 条

[1] EQUIVALENCE OF 2 DEFINITIONS OF CAPACITY
ADAMS, DR
POLKING, JC
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 37 (02) : 529 - 534
[2] EXISTENCE OF CAPACITARY STRONG TYPE ESTIMATES IN RN
ADAMS, DR
[J]. ARKIV FOR MATEMATIK, 1976, 14 (01): : 125 - 140
[3] BARAS P, UNPUB PROBLEMES PARA
[4] BARAS P, 1984, ANN I FOURIER GRENOB, V34, P1
[5] FUJITA H, 1966, J FAC SCI U TOKYO 1, V13, P109
[6] Lions J.-L., 1969, QUELQUES METHODES RE
[7] THEORY OF CAPACITIES FOR POTENTIALS OF FUNCTIONS IN LEBESGUE CLASSES
MEYERS, NG
[J]. MATHEMATICA SCANDINAVICA, 1970, 26 (02) : 255 - &
[8] Nirenberg L., 1959, ANN SCUOLA NORM-SCI, V13, P115
[9] PIERRE M, 1983, SEMINAIRE GOULAOUICM
[10] Schaefer H. H., 1971, TOPOLOGICAL VECTOR S

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