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Positive Solutions for the Generalized Nonlinear Logistic Equations

  Published:2015-12-12
 Printed: Mar 2016
  • Leszek Gasiński,
    Jagiellonian University, Faculty of Mathematics and Computer Science, , ul. Łojasiewicza 6, 30-348 Kraków, Poland
  • Nikolaos S. Papageorgiou,
    National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
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Abstract

We consider a nonlinear parametric elliptic equation driven by a nonhomogeneous differential operator with a logistic reaction of the superdiffusive type. Using variational methods coupled with suitable truncation and comparison techniques, we prove a bifurcation type result describing the set of positive solutions as the parameter varies.
Keywords: positive solution, bifurcation type result, strong comparison principle, nonlinear regularity, nonlinear maximum principle positive solution, bifurcation type result, strong comparison principle, nonlinear regularity, nonlinear maximum principle
MSC Classifications: 35J25, 35J92 show english descriptions Boundary value problems for second-order elliptic equations
Quasilinear elliptic equations with $p$-Laplacian
35J25 - Boundary value problems for second-order elliptic equations
35J92 - Quasilinear elliptic equations with $p$-Laplacian
 

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