# Inequality Estimates of an Inhomogeneous Semilinear Biharmonic Equation in Entire Space

Inequality Estimates of an Inhomogeneous Semilinear Biharmonic Equation in Entire Space In this paper, we consider the inequality estimates of the positive solutions for the inhomogeneous biharmonic equation $$-\Delta^{2} u+u^{p}+f(x)=0 \; \rm{in} \; \mathbb{R}^{n},$$ − Δ 2 u + u p + f ( x ) = 0 i n R n , where Δ2 is the biharmonic operator, p > 1, n ≥ 5 and 0 ≢ f ∈ C(ℝ n ) is a given nonnegative function. We obtain different inequality estimates of Eq.(*), with which the necessary conditions of existence on f and p are also established. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Inequality Estimates of an Inhomogeneous Semilinear Biharmonic Equation in Entire Space

, Volume 35 (4) – Dec 19, 2019
8 pages

/lp/springer-journals/inequality-estimates-of-an-inhomogeneous-semilinear-biharmonic-vsUEnFkSx0
Publisher
Springer Journals
Copyright © 2019 by The Editorial Office of AMAS & Springer-Verlag GmbH Germany
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-019-0854-2
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we consider the inequality estimates of the positive solutions for the inhomogeneous biharmonic equation $$-\Delta^{2} u+u^{p}+f(x)=0 \; \rm{in} \; \mathbb{R}^{n},$$ − Δ 2 u + u p + f ( x ) = 0 i n R n , where Δ2 is the biharmonic operator, p > 1, n ≥ 5 and 0 ≢ f ∈ C(ℝ n ) is a given nonnegative function. We obtain different inequality estimates of Eq.(*), with which the necessary conditions of existence on f and p are also established.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Dec 19, 2019

### References

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