Monotonicity of the forcing term and existence of positive solutions for a class of semilinear elliptic problems
Monotonicity of the forcing term and existence of positive solutions for a class of semilinear elliptic problems
We study the existence of positive solutions to the equation<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Delta u plus f left-parenthesis u right-parenthesis plus lamda g left-parenthesis double-vertical-bar x double-vertical-bar right-parenthesis equals 0"><mml:semantics><mml:mrow><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 stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>λ<!-- λ --></mml:mi><mml:mi>g</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo symmetric="true">‖</mml:mo><mml:mi>x</mml:mi><mml:mo symmetric="true">‖</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:annotation encoding="application/x-tex">\Delta u + f(u) + \lambda g(\left \| …