open access

https://hdl.handle.net/2115/78730

SOLUTIONS IN LEBESGUE SPACES TO NONLINEAR ELLIPTIC EQUATIONS WITH SUBNATURAL GROWTH TERMS

英語

Green function

2020-06

American Mathematical Society

St Petersburg Mathematical Journal

31(3)

557-572

The paper is devoted to the existence problem for positive solutions u is an element of L-r(R-n), 0 < r < infinity, to the quasilinear elliptic equation -Delta(p)u = sigma u(q) in R-n in the subnatural growth case 0 < q < p - 1, where Delta(p)u = div(vertical bar del u vertical bar(P -2)del u) is the p-Laplacian with 1 < p < infinity, and sigma is a nonnegative measurable function (or measure) on R. The techniques rely on a study of general integral equations involving nonlinear potentials and related weighted norm inequalities. They are applicable to more general quasilinear elliptic operators in place of Delta(p) such as the A-Laplacian divA(x, del u), or the fractional Laplacian (-Delta)(alpha) on R-n, as well as linear uniformly elliptic operators with bounded measurable coefficients div(A del u) on an arbitrary domain Omega subset of R-n with a positive Green function.

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Accepted Manuscript

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First published in St Petersburg Mathematical Journal 31(3), published by the American Mathematical Society. ©2020 American Mathematical Society.

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