Positive solutions for superdiffusive mixed problems
Nikolaos S. Papageorgiou, Vicen\c{t}iu D. R\u{a}dulescu, and Du\v{s}an, D. Repov\v{s}
TL;DR
This paper investigates positive solutions for a semilinear elliptic equation with superdiffusive reaction terms and mixed boundary conditions, establishing conditions for their existence, nonexistence, and multiplicity using variational and bifurcation methods.
Contribution
It introduces a bifurcation theorem for positive solutions in superdiffusive elliptic problems with mixed boundary conditions, employing variational and truncation techniques.
Findings
Identifies conditions for nonexistence of solutions.
Establishes criteria for existence of solutions.
Demonstrates multiplicity of positive solutions.
Abstract
We study a semilinear parametric elliptic equation with superdiffusive reaction and mixed boundary conditions. Using variational methods, together with suitable truncation techniques, we prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions.
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