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Sufficient conditions are established for the matrix Riccati equation to have a symmetric solution on a given interval. The criteria involve integral conditions on the coefficient matrices of the Riccati equation. The present results are compared with previously known results

international journal of mathematics and mathematical sciences

Existance theroms for the matrix Riccati equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$W' + W P(t)W + Q(t) = 0$"><mml:mrow><mml:msup><mml:mi>W</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:mi>W</mml:mi><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>W</mml:mi><mml:mo>+</mml:mo><mml:mi>Q</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml…

Existance theroms for the matrix Riccati equationW′+WP(t)W+Q(t)=0