Ground state solutions to nonlinear equations with p-Laplacian
| Autoři | |
|---|---|
| Rok publikování | 2019 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://www.sciencedirect.com/science/article/pii/S0362546X19300410 |
| Doi | http://dx.doi.org/10.1016/j.na.2019.01.032 |
| Klíčová slova | Second order nonlinear differential equation; Ground state solution; Boundary value problem on the half-line |
| Popis | We investigate the existence of positive radial solutions for a nonlinear elliptic equation with p-Laplace operator and sign-changing weight, both in superlinear and sublinear case. We prove the existence of solutions u, which are globally defined and positive outside a ball of radius R, satisfy fixed initial conditions u(R) = c > 0, u' (R) = 0 and tend to zero at infinity. Our method is based on a fixed point result for boundary value problems on noncompact intervals and on asymptotic properties of suitable auxiliary half-linear differential equations. The results are new also for the classical Laplace operator and may be used for proving the existence of ground state solutions and decaying solutions with exactly k-zeros which are defined in the whole space. Some examples illustrate our results. |
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