On Entire Solutions of Quasilinear Elliptic Equations
| dc.contributor.advisor | Mohammed, Ahmed (Professor) | |
| dc.contributor.author | Araya, Ataklti | |
| dc.date.accessioned | 2018-07-12T05:27:41Z | |
| dc.date.accessioned | 2023-11-04T12:32:09Z | |
| dc.date.available | 2018-07-12T05:27:41Z | |
| dc.date.available | 2023-11-04T12:32:09Z | |
| dc.date.issued | 2017-06-28 | |
| dc.description.abstract | In this thesis, we investigate entire solutions of the quasilinear equation (y) __u = h(x; u) where __u := div(_(jruj)ru): Under suitable assumptions on the right-hand side we will show the existence of in_nitely many positive solutions that are bounded and bounded away from zero in RN: All these solutions converge to a positive constant at in_nity. The analysis that leads to these results is based on a _xed-point theorem attributed to Shcauder-Tychono_. Under appropriate assumptions on h(x; t), we will also study ground state solutions of (y) whose asymptotic behavior at in_nity is the same as a fundamental solution of the _-Laplacian operator __: Ground state solutions are positive solutions that decay to zero at in_nity. An investigation of positive solutions of (y) that converge to prescribed positive constants at in_nity will be considered when the right-hand side in (y) assumes the form h(x; t) = a(x)f(t): After establishing a general result on the construction of positive solutions that converge to positive constants, we will present simple su_cient conditions that apply to a wide class of continuous functions f : R ! R so that the equation __u = a(x)f(u) admits positive solutions that converge to prescribed positive constants at in_nity. We will also study Cauchy-Liuoville type problems associated with the equation __u = f(u) in RN: More speci_cally, we will study su_cient conditions on f : R ! R in order that the equation __u = f(u) admits only constant positive solution provided that f has at least one real root. Our result in this direction can best be illustrated by taking _(t) = ptp2 + qtq2 for some 1 < p < q which leads to the so called (p; q)-Laplacian, _(p;q)u := _pu + _qu: | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/8130 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | On Entire Solutions | en_US |
| dc.subject | of Quasilinear Elliptic | en_US |
| dc.title | On Entire Solutions of Quasilinear Elliptic Equations | en_US |
| dc.type | Thesis | en_US |