Positive solutions for a Minkowski-curvature equation with indefinite weight and super-exponential nonlinearity
| Autor: | Alberto Boscaggin, Guglielmo Feltrin, Fabio Zanolin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
positive solutions
Minkowski-curvature operator indefinite weight periodic problem Neumann problem super-exponential nonlinearity Applied Mathematics General Mathematics 34B15 34B18 34C25 47H11 Minkowski-curvature operator indefinite weight positive solutions periodic problem Neumann problem super-exponential nonlinearity Mathematics::Probability Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics |
| Popis: | We investigate the existence of positive solutions for a class of Minkowski-curvature equations with indefinite weight and nonlinear term having superlinear growth at zero and super-exponential growth at infinity. As an example, for the equation \begin{equation*} \Biggl{(} \dfrac{u'}{\sqrt{1-(u')^{2}}}\Biggr{)}' + a(t) \bigl{(}e^{u^{p}}-1\bigr{)} = 0, \end{equation*} where $p > 1$ and $a(t)$ is a sign-changing function satisfying the mean-value condition $\int_{0}^{T} a(t)\,\mathrm{d}t < 0$, we prove the existence of a positive solution for both periodic and Neumann boundary conditions. The proof relies on a topological degree technique. 19 pages, 3 figures |
| Databáze: | OpenAIRE |
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