Existence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth condition
โ Scribed by Mashiyev, R.A.; Cekic, B.; Avci, M.; Yucedag, Z.
- Book ID
- 120167320
- Publisher
- Taylor and Francis Group
- Year
- 2012
- Tongue
- English
- Weight
- 179 KB
- Volume
- 57
- Category
- Article
- ISSN
- 1747-6933
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๐ SIMILAR VOLUMES
## Abstract We prove a removability result for nonlinear elliptic equations with__p__ (__x__)โtype nonstandard growth and estimate the growth of solutions near a nonremovable isolated singularity. To accomplish this, we employ a Harnack estimate for possibly unbounded solutions and the fact that so
Let \(\Omega\) be a smooth bounded domain of \(\mathbb{R}^{n}, n \geqslant 3\), and let \(a(x)\) and \(f(x)\) be two smooth functions defined on a neighbourhood of \(\Omega\). First we study the existence of nodal solutions for the equation \(\Delta u+a(x) u=f(x)|u|^{4 /(n-2)} u\) on \(\Omega, u=0\)