Taiwanese Journal of Mathematics


Maria-Magdalena Boureanu

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We study the nonlinear degenerate problem $-\sum_{i=1}^N \partial_{x_i} a_i \left(x,\partial_{x_i}u \right) = f(x,u)$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega \subset {\mathbb R}^N$ ($N \geq 3$) is a bounded domain with smooth boundary, $\sum_{i=1}^N \partial_{x_i} a_i \left(x,\partial_{x_i}u \right)$ is a $\overset{\rightarrow} p(\cdot)$ - Laplace type operator and the nonlinearity $f$ is $(P_+^+-1)$ - superlinear at infinity (with $\overset{\rightarrow} p(x) = (p_1(x), p_2(x), ... p_N(x))$ and $P_+^+ = \max_{i \in \{1,...,N\}} \left\{\sup_{x \in \Omega} p_i(x) \right\}$). By means of the symmetric mountain-pass theorem of Ambrosetti and Rabinowitz, we establish the existence of a sequence of weak solutions in appropriate anisotropic variable exponent Sobolev spaces.

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Taiwanese J. Math., Volume 15, Number 5 (2011), 2291-2310.

First available in Project Euclid: 18 July 2017

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Primary: 35J25: Boundary value problems for second-order elliptic equations 35J62: Quasilinear elliptic equations 35D30: Weak solutions 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 35J20: Variational methods for second-order elliptic equations

quasilinear elliptic equations multiple weak solutions critical point theory anisotropic variable exponent Sobolev spaces symmetric mountain-pass theorem


Boureanu, Maria-Magdalena. INFINITELY MANY SOLUTIONS FOR A CLASS OF DEGENERATE ANISOTROPIC ELLIPTIC PROBLEMS WITH VARIABLE EXPONENT. Taiwanese J. Math. 15 (2011), no. 5, 2291--2310. doi:10.11650/twjm/1500406435. https://projecteuclid.org/euclid.twjm/1500406435

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