کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4589664 1334896 2016 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Gaps of consecutive eigenvalues of Laplace operator and the existence of multiple solutions for superlinear elliptic problem
ترجمه فارسی عنوان
شکافهای مقادیر متوالی اپراتور لاپلاس و وجود راه حل های چندگانه برای مسئله بیضوی فوق العاده خطی
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

This paper is mainly related to multiple nontrivial solutions of the elliptic boundary value problem{−Δu=|u|p−2u+f(x,u),x∈Ω,u=0,x∈∂Ω, for p∈(2,2⁎)p∈(2,2⁎). It is reasonable to guess that for dim⁡Ω≥2dim⁡Ω≥2 above problem possesses infinitely many distinct solutions since this is proved to be true for ODE. However, so far one does not even know if there exists a fourth nontrivial solution. By using a new homological linking theorem, Morse theory, and some precise estimates we disclose the relationship among the gaps of consecutive eigenvalues of Laplace operator, growth trend of nonlinear terms and the existence of multiple solutions of superlinear elliptic boundary value problem. Moreover, as p   is close to 2, we get the fourth nontrivial solution under appropriate hypotheses, where f(x,u)f(x,u) satisfies Ambrosetti–Rabinowitz condition.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 271, Issue 2, 15 July 2016, Pages 245–263
نویسندگان
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