Number of solutions with a norm bounded by a given constant of a semilinear elliptic PDE with a generic right-hand side
Number of solutions with a norm bounded by a given constant of a semilinear elliptic PDE with a generic right-hand side
We consider a semilinear boundary value problem <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="minus normal upper Delta u plus f left-parenthesis u comma x right-parenthesis equals 0"> <mml:semantics> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mi mathvariant="normal">Δ<!-- Δ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">- \Delta …