Positive solutions for a class of semipositone periodic boundary value problems via bifurcation theory
In this paper, we are concerned with the existence of positive solutions of nonlinear periodic boundary value problems like − u 00 + q(x)u = λ f(x, u), x ∈ (0, 2π), u(0) = u(2π), u 0 (0) = u 0 (2π), where q ∈ C([0, 2π], [0, ∞)) with q 6≡ 0, f ∈ C([0, 2π] × R+, R), λ > 0 is the bifurcation paramet...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Határérték probléma - differenciálegyenletek, Bifurkációelmélet |
| doi: | 10.14232/ejqtde.2019.1.29 |
| Online Access: | http://acta.bibl.u-szeged.hu/62107 |
| Tartalmi kivonat: | In this paper, we are concerned with the existence of positive solutions of nonlinear periodic boundary value problems like − u 00 + q(x)u = λ f(x, u), x ∈ (0, 2π), u(0) = u(2π), u 0 (0) = u 0 (2π), where q ∈ C([0, 2π], [0, ∞)) with q 6≡ 0, f ∈ C([0, 2π] × R+, R), λ > 0 is the bifurcation parameter. By using bifurcation theory, we deal with both asymptotically linear, superlinear as well as sublinear problems and show that there exists a global branch of solutions emanating from infinity. Furthermore, we proved that for λ near the bifurcation value, solutions of large norm are indeed positive. |
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| Terjedelem/Fizikai jellemzők: | 1-15 |
| ISSN: | 1417-3875 |