On a superlinear elliptic boundary value problem at resonance

Abstract

Semilinear partial differential equations of the type <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="minus normal upper Delta u minus lamda 2 u plus e Superscript u Baseline equals h"> <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:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>λ<!-- λ --></mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>e</mml:mi> <mml:mi>u</mml:mi> </mml:msup> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>h</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">- \Delta u - {\lambda _2}u + {e^u} = h</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are studied and existence and multiplicity results obtained.

Locations

• Proceedings of the American Mathematical Society - View - PDF