论文标题
具有无限重量和超指定性非线性的Minkowski-curvature方程的正溶液
Positive solutions for a Minkowski-curvature equation with indefinite weight and super-exponential nonlinearity
论文作者
论文摘要
我们调查了一类Minkowski曲面方程的阳性溶液的存在，其重量不确定和非线性术语在无限时具有超线性生长和超级指数生长。例如，对于方程式\ begin {equination*} \ bigGl {（} \ dfrac {u'} {\ sqrt {\ sqrt {1-（u'）^{2}}}}} \ biggr {）} \ end {equation*}其中$ p> 1 $和$ a（t）$是满足平均值条件$ \ int_ {0}^{t} a（t）\，\ mathrm {d} t <0 $，我们证明存在于两个周期性和neumann neyumann sourcy的积极解决方案。证明依赖于拓扑学位技术。
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.
