## Topological Methods in Nonlinear Analysis

### Solutions of implicit evolution inclusions with pseudo-monotone mappings

Wenming M. Bian

#### Abstract

Existence results are given for the implicit evolution inclusions $(Bx(t))'+A(t,x(t))\ni f(t)$ and $(Bx(t))'+A(t,x(t))-G(t,x(t))\ni f(t)$ with $B$ a bounded linear operator, $A(t,\cdot)$ a bounded, coercive and pseudo-monotone set-valued mapping and $G$ a set-valued mapping of non-monotone type. Continuity of the solution set of first inclusion with respect to $f$ is also obtained which is used to solve the second inclusion.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 15, Number 1 (2000), 101-113.

Dates
First available in Project Euclid: 22 August 2016

https://projecteuclid.org/euclid.tmna/1471873910

Mathematical Reviews number (MathSciNet)
MR1786254

Zentralblatt MATH identifier
0970.34058

#### Citation

Bian, Wenming M. Solutions of implicit evolution inclusions with pseudo-monotone mappings. Topol. Methods Nonlinear Anal. 15 (2000), no. 1, 101--113. https://projecteuclid.org/euclid.tmna/1471873910