Positive solutions for a second-order \Phi-Laplacian equations with limiting nonlocal boundary conditions
Motivated, mainly, by the works of Fewster-Young and Tisdell [9,10] and Orpel [30], as well as the papers by Karakostas [21,22,23], we give sufficient conditions to guarantee the existence of (nontrivial) solutions of the second-order Phi-Laplacian equation $$ \frac{1}{p(t)}\frac{d}{dt}[p(t)...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/251/abstr.html |
| _version_ | 1819224823327358976 |
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| author | George L. Karakostas Konstantina G. Palaska Panagiotis Ch. Tsamatos |
| author_facet | George L. Karakostas Konstantina G. Palaska Panagiotis Ch. Tsamatos |
| author_sort | George L. Karakostas |
| collection | DOAJ |
| description | Motivated, mainly, by the works of Fewster-Young and Tisdell [9,10]
and Orpel [30], as well as the papers by Karakostas [21,22,23],
we give sufficient conditions to guarantee the existence of (nontrivial)
solutions of the second-order Phi-Laplacian equation
$$
\frac{1}{p(t)}\frac{d}{dt}[p(t)\Phi(u'(t))]+(Fu)(t)=0,\quad\text{a.e. }
t\in[0,1]=:I,
$$
which satisfy the nonlocal boundary value conditions of the
limiting Sturm-Liouville form
$$
\lim_{t\to 0}[p(t)\Phi(u'(t))]=\int_0^1u(s)d\eta(s),\quad
\lim_{t\to 1}[p(t)\Phi(u'(t))]=-\int_0^1u(s)d\zeta(s).
$$
Here $\Phi$ is an increasing homeomorphism of the real line onto itself
and F is an operator acting on the function u and on its first
derivative with the characteristic property that $u\to p(Fu)$ is a
$C^0$-type, or $C^1$-type Caratheodory operator, a meaning introduced here.
Examples are given to illustrate both cases. |
| first_indexed | 2024-12-23T09:59:49Z |
| format | Article |
| id | doaj.art-d73c0a282e9c40789098362fd8090fae |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-23T09:59:49Z |
| publishDate | 2016-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-d73c0a282e9c40789098362fd8090fae2022-12-21T17:51:17ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-09-012016251,117Positive solutions for a second-order \Phi-Laplacian equations with limiting nonlocal boundary conditionsGeorge L. Karakostas0Konstantina G. Palaska1Panagiotis Ch. Tsamatos2 Univ. of Ioannina, Greece Univ. of Ioannina, Greece Univ. of Ioannina, Greece Motivated, mainly, by the works of Fewster-Young and Tisdell [9,10] and Orpel [30], as well as the papers by Karakostas [21,22,23], we give sufficient conditions to guarantee the existence of (nontrivial) solutions of the second-order Phi-Laplacian equation $$ \frac{1}{p(t)}\frac{d}{dt}[p(t)\Phi(u'(t))]+(Fu)(t)=0,\quad\text{a.e. } t\in[0,1]=:I, $$ which satisfy the nonlocal boundary value conditions of the limiting Sturm-Liouville form $$ \lim_{t\to 0}[p(t)\Phi(u'(t))]=\int_0^1u(s)d\eta(s),\quad \lim_{t\to 1}[p(t)\Phi(u'(t))]=-\int_0^1u(s)d\zeta(s). $$ Here $\Phi$ is an increasing homeomorphism of the real line onto itself and F is an operator acting on the function u and on its first derivative with the characteristic property that $u\to p(Fu)$ is a $C^0$-type, or $C^1$-type Caratheodory operator, a meaning introduced here. Examples are given to illustrate both cases.http://ejde.math.txstate.edu/Volumes/2016/251/abstr.htmlPositive solutionSturm-Liouville equationPhi-LaplacianSchauder's fixed point theorem |
| spellingShingle | George L. Karakostas Konstantina G. Palaska Panagiotis Ch. Tsamatos Positive solutions for a second-order \Phi-Laplacian equations with limiting nonlocal boundary conditions Electronic Journal of Differential Equations Positive solution Sturm-Liouville equation Phi-Laplacian Schauder's fixed point theorem |
| title | Positive solutions for a second-order \Phi-Laplacian equations with limiting nonlocal boundary conditions |
| title_full | Positive solutions for a second-order \Phi-Laplacian equations with limiting nonlocal boundary conditions |
| title_fullStr | Positive solutions for a second-order \Phi-Laplacian equations with limiting nonlocal boundary conditions |
| title_full_unstemmed | Positive solutions for a second-order \Phi-Laplacian equations with limiting nonlocal boundary conditions |
| title_short | Positive solutions for a second-order \Phi-Laplacian equations with limiting nonlocal boundary conditions |
| title_sort | positive solutions for a second order phi laplacian equations with limiting nonlocal boundary conditions |
| topic | Positive solution Sturm-Liouville equation Phi-Laplacian Schauder's fixed point theorem |
| url | http://ejde.math.txstate.edu/Volumes/2016/251/abstr.html |
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