标题： 关于具有无通量边界条件的$p(\cdot)$-双调和问题 显示英文标题

标题： On a $p(\cdot)$-biharmonic problem with no-flux boundary condition

摘要： 第四阶偏微分方程的研究在近年来得到了蓬勃发展，然而，具有无通量边界条件的$p(\cdot)$-双调和问题之前从未被考虑过，甚至对于常数$p$也是如此。 这是一个重要的进一步步骤，因为对某些污染物不渗透的表面在自然界中经常出现，因此这种边界条件具有重要意义。 通过依赖于多个变分论证，我们获得了我们问题的弱解的存在性和多重性。 我们指出，尽管我们使用了一种山路类型定理来建立多重性结果，但我们的非线性项$f$上并未施加 Ambrosetti-Rabinowitz 类型条件，也未施加对称性条件。 显示英文摘要

摘要： The study of fourth order partial differential equations has flourished in the last years, however, a $p(\cdot)$-biharmonic problem with no-flux boundary condition has never been considered before, not even for constant $p$. This is an important step further, since surfaces that are impermeable to some contaminants are appearing quite often in nature, hence the significance of such boundary condition. By relying on several variational arguments, we obtain the existence and the multiplicity of weak solutions to our problem. We point out that, although we use a mountain pass type theorem in order to establish the multiplicity result, we do not impose an Ambrosetti-Rabinowitz type condition, nor a symmetry condition, on our nonlinearity $f$.