Second-order ordinary differential equations with indefinite weight: the Neumann boundary value problem
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| 024 | 7 | 0 | |a 10.1007/s10231-013-0384-0 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-013-0384-0 | ||
| 245 | 0 | 0 | |a Second-order ordinary differential equations with indefinite weight: the Neumann boundary value problem |h [Elektronische Daten] |c [Alberto Boscaggin, Fabio Zanolin] |
| 520 | 3 | |a We study the second-order nonlinear differential equation $$u'' + a(t) g(u) = 0$$ u ′ ′ + a ( t ) g ( u ) = 0 , where $$g$$ g is a continuously differentiable function of constant sign defined on an open interval $$I\subseteq {\mathbb R}$$ I ⊆ R and $$a(t)$$ a ( t ) is a sign-changing weight function. We look for solutions $$u(t)$$ u ( t ) of the differential equation such that $$u(t)\in I,$$ u ( t ) ∈ I , satisfying the Neumann boundary conditions. Special examples, considered in our model, are the equations with singularity, for $$I = {\mathbb R}^+_0$$ I = R 0 + and $$g(u) \sim - u^{-\sigma },$$ g ( u ) ∼ - u - σ , as well as the case of exponential nonlinearities, for $$I = {\mathbb R}$$ I = R and $$g(u) \sim \exp (u)$$ g ( u ) ∼ exp ( u ) . The proofs are obtained by passing to an equivalent equation of the form $$x'' = f(x)(x')^2 + a(t)$$ x ′ ′ = f ( x ) ( x ′ ) 2 + a ( t ) . | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 | ||
| 690 | 7 | |a Boundary value problems |2 nationallicence | |
| 690 | 7 | |a Indefinite weight |2 nationallicence | |
| 690 | 7 | |a Necessary and sufficient solvability conditions |2 nationallicence | |
| 700 | 1 | |a Boscaggin |D Alberto |u Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123, Torino, Italy |4 aut | |
| 700 | 1 | |a Zanolin |D Fabio |u Department of Mathematics and Computer Science, University of Udine, Via delle Scienze 206, 33100, Udine, Italy |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/2(2015-04-01), 451-478 |x 0373-3114 |q 194:2<451 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-013-0384-0 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-013-0384-0 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Boscaggin |D Alberto |u Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123, Torino, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zanolin |D Fabio |u Department of Mathematics and Computer Science, University of Udine, Via delle Scienze 206, 33100, Udine, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/2(2015-04-01), 451-478 |x 0373-3114 |q 194:2<451 |1 2015 |2 194 |o 10231 | ||