PERTURBATIONS FROM INDEFINITE SYMMETRIC ELLIPTIC BOUNDARY VALUE PROBLEMS
Glasgow mathematical journal, Tome 59 (2017) no. 3, pp. 635-648
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In this paper, we study the multiplicity of solutions for the following problem: $$\begin{equation*}\begin{cases}-\Delta u-\Delta(|u|^{\alpha})|u|^{\alpha-2}u=g(x,u)+\theta h(x,u), \ \ x\in \Omega,\\u=0, \ \ x\in \partial\Omega,\end{cases}\end{equation*}$$ where α ≥ 2, Ω is a smooth bounded domain in ${\mathbb{R}}$ N , θ is a parameter and g, h ∈ C( $\bar{\Omega}$ × ${\mathbb{R}}$ ). Under the assumptions that g(x, u) is odd and locally superlinear at infinity in u, we prove that for any j ∈ $\mathbb{N}$ there exists εj > 0 such that if |θ| ≤ εj , the above problem possesses at least j distinct solutions. Our results generalize some known results in the literature and are new even in the symmetric situation.
ZHANG, LIANG; TANG, XIANHUA. PERTURBATIONS FROM INDEFINITE SYMMETRIC ELLIPTIC BOUNDARY VALUE PROBLEMS. Glasgow mathematical journal, Tome 59 (2017) no. 3, pp. 635-648. doi: 10.1017/S0017089516000446
@article{10_1017_S0017089516000446,
author = {ZHANG, LIANG and TANG, XIANHUA},
title = {PERTURBATIONS {FROM} {INDEFINITE} {SYMMETRIC} {ELLIPTIC} {BOUNDARY} {VALUE} {PROBLEMS}},
journal = {Glasgow mathematical journal},
pages = {635--648},
year = {2017},
volume = {59},
number = {3},
doi = {10.1017/S0017089516000446},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000446/}
}
TY - JOUR AU - ZHANG, LIANG AU - TANG, XIANHUA TI - PERTURBATIONS FROM INDEFINITE SYMMETRIC ELLIPTIC BOUNDARY VALUE PROBLEMS JO - Glasgow mathematical journal PY - 2017 SP - 635 EP - 648 VL - 59 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000446/ DO - 10.1017/S0017089516000446 ID - 10_1017_S0017089516000446 ER -
%0 Journal Article %A ZHANG, LIANG %A TANG, XIANHUA %T PERTURBATIONS FROM INDEFINITE SYMMETRIC ELLIPTIC BOUNDARY VALUE PROBLEMS %J Glasgow mathematical journal %D 2017 %P 635-648 %V 59 %N 3 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000446/ %R 10.1017/S0017089516000446 %F 10_1017_S0017089516000446
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