# On the existence and uniqueness of positive solutions of some mildly nonlinear elliptic boundary value problems

## Abstract

For a homogeneous Dirichlet problem attached to a semilinear elliptic equation we study the existence and uniqueness of non-negative solutions. Our analysis is based on  straightforward use of Schauder’s fixed point principle for existence and comparatively, based on the Banach’s contraction principle and on a generalized maximum principle for the uniqueness. We have obtained two independent conditions for uniqueness of solution. Both depend on the geometry of the domain as well as on the parameters of the problem.

## Authors

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

Al. Tămăşan
Babeş-Bolyai University, Cluj-Napoca, Romania

## Keywords

boundary value problem; elliptic; quadratic nonlinearity; non-negative solution; existence; uniqueness; Schauder fixed point; Banach contraction; generalized maximum ;

### References

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## Cite this paper as

C.I. Gheorghiu, Al. Tămăşan, On the existence and uniqueness of positive solutions of some mildly nonlinear elliptic boundary value problems, Rev. Anal. Numér. Théor. Approx. 24 (1995), pp. 125-129.

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##### Journal

Rev. Anal. Numér. Théor. Approx.

1222-9024

2457-8126

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