Vol. 57, No. 1, 1975

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ISSN: 0030-8730
On bounded solutions of a strongly nonlinear elliptic equation

Nguyên Phuong Các

Vol. 57 (1975), No. 1, 53–58
Abstract

I. Introduction. Consider the Dirichlet problem for a bounded domain G Rn(n 2) having smooth boundary ∂G:

𝒜u + p(u) = − Difi + f
z|∂G = 0,
(1)

where 𝒜 is a second order differential operator of Leray-Lions type mapping a real Sobolev space W01q(G)(1 < q < ) into its dual; f,fi(i = 1,,n) are given functions. We have used the notation Di for the derivative in the distribution sense ∂∕∂xi and the convention that if an index is repeated then summation over that index from 1 to n is implied. We shall assume that the real function p(t) is continuous and satisfies the condition

p(t)t ≧ 0 ∀t ∈ R,
(2)

but otherwise (p)t is not subject to any growth condition.

In this paper we discuss the existence of a solution of equation (1) in W01,q(G) L(G).

Mathematical Subject Classification 2000
Primary: 35J65
Milestones
Received: 15 October 1974
Published: 1 March 1975
Authors
Nguyên Phuong Các