A class of elliptic equations involving nonlocal integrodifferential operators with sign-changing weight functions

2020 ◽  
Vol 61 (5) ◽  
pp. 051503
Author(s):  
L. M. M. Bonaldo ◽  
E. J. Hurtado ◽  
O. H. Miyagaki
Keyword(s):  
Elliptic Equations ◽  
Weight Functions ◽  
Integrodifferential Operators

scholarly journals Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Tsing-San Hsu
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equation ◽  
Nehari Manifold ◽  
Weight Functions ◽  
Multiple Positive Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions ◽  
The Nehari Manifold

Existence and multiplicity of positive solutions for the following semilinear elliptic equation: in , , are established, where if if , , satisfy suitable conditions, and maybe changes sign in . The study is based on the extraction of the Palais-Smale sequences in the Nehari manifold.

scholarly journals Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 5
Author(s):  
Jun Ik Lee ◽  
Yun-Ho Kim ◽  
Jongrak Lee
Keyword(s):  
Elliptic Equations ◽  
Mountain Pass Theorem ◽  
Functional Method ◽  
Fountain Theorem ◽  
Small Energy ◽  
Localization Method ◽  
Dual Version ◽  
Symmetric Mountain Pass Theorem ◽  
Integrodifferential Operators ◽  
Modified Functional

We are concerned with the following elliptic equations: ( − Δ ) p , K s u + V ( x ) | u | p − 2 u = λ f ( x , u ) in R N , where ( − Δ ) p , K s is the nonlocal integrodifferential equation with 0 < s < 1 < p < + ∞ , s p < N the potential function V : R N → ( 0 , ∞ ) is continuous, and f : R N × R → R satisfies a Carathéodory condition. The present paper is devoted to the study of the L ∞ -bound of solutions to the above problem by employing De Giorgi’s iteration method and the localization method. Using this, we provide a sequence of infinitely many small-energy solutions whose L ∞ -norms converge to zero. The main tools were the modified functional method and the dual version of the fountain theorem, which is a generalization of the symmetric mountain-pass theorem.

scholarly journals Multiple Positive Solutions for Semilinear Elliptic Equations in Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Tsing-San Hsu ◽  
Huei-Li Lin
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic Equations ◽  
Weight Functions ◽  
Multiple Positive Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation in , , where , if , if ), , satisfy suitable conditions, and may change sign in .

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