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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 14
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 14, Issue 3-4, November 2007
  4. Periodic parabolic problems with concave and convex nonlinearities
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 14, Issue 5-6, December 2007
Nonlinear Differential Equations and Applications NoDEA : Volume 14, Issue 3-4, November 2007
Hamilton-Jacobi methods for Vakonomic Mechanics
Existence, uniqueness and regularity for nonlinear parabolic equations with nonlocal terms
Multiple solutions of a sublinear Schrödinger equation
On a class of coupled elliptic systems in $${\mathbb{R}}^{N}$$
Some results on the qualitative properties of positive solutions of quasilinear elliptic equations
The effect of Harnack inequality on the existence and nonexistence results for quasi-linear parabolic equations related to Caffarelli-Kohn-Nirenberg inequalities
Multivalued evolution equations with nonlocal initial conditions in Banach spaces
Local Lipschitz continuity of graphs with prescribed Levi mean curvature
Uniqueness and comparison properties of the viscosity solution to some singular HJB equations
Compactness results for $${\mathcal{L}}^{\infty}$$ -solution operator of a linear evolution equation involving measures
Limiting behavior of solutions of subelliptic heat equations
Periodic parabolic problems with concave and convex nonlinearities
Nonlinear Differential Equations and Applications NoDEA : Volume 14, Issue 1-2, October 2007
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Periodic parabolic problems with concave and convex nonlinearities

Content Provider SpringerLink
Author Kaufmann, U. Godoy, T.
Copyright Year 2007
Abstract Let $$\Omega \subset {\mathbb{R}}^N$$ be a smooth bounded domain, let a, b be two functions that are possibly discontinuous and unbounded with a ≥ 0 in $$\Omega\times{\mathbb{R}}$$ and b > 0 in a set of positive measure and let 0 < p < 1 < q. We prove that there exists some 0 < Λ < ∞ such that the nonlinear Dirichlet periodic parabolic problem $$Lu = \lambda a (x, t) u^p + b (x, t) u^q$$ in $$\Omega \times {\mathbb{R}}$$ has a positive solution for all 0 < λ < Λ and that there is no positive solution if λ > Λ. In some cases we also show the existence of a minimal solution for all 0 < λ < Λ and that the solution u λ can be chosen such that λ → u λ is differentiable and increasing. We also give some upper and lower estimates for such a Λ. All results remain true for the analogous elliptic problems.
Ending Page 453
Page Count 11
Starting Page 443
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 3
Volume Number 14
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2007-09-21
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword concave parabolic Initial-boundary value problems for second-order parabolic equations Periodic solutions periodic Analysis convex General topics in linear spectral theory
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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