MULTIPLE POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS WITH WEIGHT FUNCTION IN EXTERIOR DOMAINS

Michinori Ishiwata

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MULTIPLE POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS WITH WEIGHT FUNCTION IN EXTERIOR DOMAINS

机译：外部域中具有权函数的半线性椭圆型方程的多重正解

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In this paper, we are concerned with the multiplicity of solutions for semilinear elliptic problems with weight functions in exterior domains. We prove that, if the decay of the weight function at spatial infinity is sufficiently slow, then the equation admits at least three solutions and two of them escape away to the spatial infinity as the decay rate of the weight function tends to 0. The result is proved via the variational method combined with the Ljusternik{Schnirelman-type multiplicity theorem.

机译：在本文中，我们关注具有外部区域权重函数的半线性椭圆问题的解的多重性。我们证明，如果权函数在空间无穷大处的衰减足够慢，则该方程至少接受三个解，并且随着权函数的衰减率趋于0，其中的两个逃逸到空间无穷大。结果通过变分方法结合Ljusternik {Schnirelman型多重性定理证明。

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《Differential and integral equations》 |2013年第2期|共18页
作者
Michinori Ishiwata;
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正文语种 eng
中图分类微分方程、积分方程;
关键词
MULTIPLE; POSITIVE; EXTERIOR;

机译：多;正;外部;

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专利

1. MULTIPLE POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS WITH WEIGHT FUNCTION IN EXTERIOR DOMAINS [J] . Michinori Ishiwata Differential and integral equations . 2013,第1a2期

机译：外部域中具有权函数的半线性椭圆型方程的多重正解
2. Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions inℝN [J] . Tsing-SanHsu Abstract and applied analysis . 2011,第6期

机译：符号线性权函数inℝN的半线性椭圆型方程的多个正解
3. Multiple Positive Solutions for Semilinear Elliptic Equations inℝNInvolving Concave-Convex Nonlinearities and Sign-Changing Weight Functions [J] . Tsing-SanHsu, Huei-LiLin Abstract and applied analysis . 2010,第4期

机译：包含凹-凸非线性和符号改变权重函数的ℝN半椭圆形方程的多个正解
4. A UNIQUE POSITIVE SOLUTION TO A SYSTEM OF SEMILINEAR ELLIPTIC EQUATIONS [C] . Diane Denny AIMS International Conference on Dynamical Systems, Differential Equations and Applications . 2013

机译：半线性椭圆方程系统的独特阳性解决方案
5. Existence and bifurcation of multiple positive solutions for some semilinear elliptic equations. [D] . Zhao, Xuejin. 1998

机译：一类半线性椭圆型方程的多个正解的存在性和分歧。
6. Existence of anti-periodic (differentiable) mild solutions to semilinear differential equations with nondense domain [O] . Jinghuai Liu, Litao Zhang -1

机译：具有稠密域的半线性微分方程的反周期（可微）温和解的存在性
7. Multiple Positive Solutions for a Class of Concave-Convex Semilinear Elliptic Equations in Unbounded Domains with Sign-Changing Weights [O] . Tsing-San Hsu 2010

机译：带符号改变权重的无界域中一类凹凸半线性椭圆型方程的多重正解
8. Some Qualitative Properties of Solutions of Semilinear Elliptic Equations inCylindrical Domains [R] . Berestycki, H., Nirenberg, L. 1990

机译：圆柱域中半线性椭圆方程解的一些定性性质

MULTIPLE POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS WITH WEIGHT FUNCTION IN EXTERIOR DOMAINS

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