Existence of solutions of a nonlinear differential equation
Existence of solutions of a nonlinear differential equation
A criterion is proved for the existence of at least one solution to the equation <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u plus u equals g left-parenthesis u right-parenthesis plus h"> <mml:semantics> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>g</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>h</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">u + u = g(u) …