Advances in Differential Equations

On the number of positive solutions for nonhomogeneous semilinear elliptic problem

Daomin Cao and J. Chabrowski

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Abstract

We prove the existence of $\text{ cat } \Omega +1$ positive solutions of problem (1). If $\text{ cat } \Omega >1$ then we establish the existence of $\text{ cat } \Omega +2$ positive solutions. The proofs are based on the Lusternik-Schnirelman theory of critical points.

Article information

Source
Adv. Differential Equations Volume 1, Number 5 (1996), 753-772.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366896018

Mathematical Reviews number (MathSciNet)
MR1392004

Zentralblatt MATH identifier
0851.35039

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 58E15: Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.

Citation

Cao, Daomin; Chabrowski, J. On the number of positive solutions for nonhomogeneous semilinear elliptic problem. Adv. Differential Equations 1 (1996), no. 5, 753--772. https://projecteuclid.org/euclid.ade/1366896018.


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