scholarly journals Existence and Nonexistence for Elliptic Equation with Cylindrical Potentials, Subcritical Exponent and Concave Term

2015 ◽  
Vol 03 (02) ◽  
Author(s):  
Mohamed El Mokhtar Ould El Mokhtar
Keyword(s):  
Elliptic Equation ◽  
Existence And Nonexistence ◽  
Concave Term

Entire Large Solutions to Elliptic Equations of Power Non-linearities with Variable Exponents

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Alan V. Lair ◽  
Ahmed Mohammed
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Elliptic Equations ◽  
Variable Exponent ◽  
Variable Exponents ◽  
Large Solutions ◽  
Existence And Nonexistence

AbstractWe give conditions on the variable exponent q that ensure the existence and nonexistence of a positive solution to the elliptic equation Δu = u

scholarly journals A nonexistence result for a nonlinear elliptic equation with singular and decaying potential

2015 ◽  
Vol 17 (04) ◽  
pp. 1450024 ◽  
Author(s):  
Marino Badiale ◽  
Michela Guida ◽  
Sergio Rolando
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Nonlinear Elliptic Equation ◽  
Negative Answer ◽  
Radial Solutions ◽  
Compatibility Conditions ◽  
Nonlinear Elliptic ◽  
Nonexistence Result ◽  
Open Case ◽  
Existence And Nonexistence

Several existence and nonexistence results are known for positive solutions u ∈ D1,2(ℝN) ∩ L2(ℝN, ∣x∣-αdx) ∩ Lp(ℝN) to the equation [Formula: see text] resting upon compatibility conditions between α and p. Letting 2α := 2N/(N - α) and [Formula: see text], the problem is still open for 0 < α < 2 and [Formula: see text], for 2 < α < N and [Formula: see text], and for N ≤ α < 2N - 2 and [Formula: see text]. Here we give a negative answer to the problem of the existence of radial solutions in the first open case.

scholarly journals The Solvability of Fractional Elliptic Equation with the Hardy Potential

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Siyu Gao ◽  
Shuibo Huang ◽  
Qiaoyu Tian ◽  
Zhan-Ping Ma
Keyword(s):  
Elliptic Equation ◽  
Lipschitz Domain ◽  
Sobolev Inequality ◽  
Elliptic Equations ◽  
Sharp Constant ◽  
Hardy Potential ◽  
Bounded Lipschitz Domain ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions ◽  
Fractional Laplace Operator

In this paper, we study the existence and nonexistence of solutions to fractional elliptic equations with the Hardy potential −Δsu−λu/x2s=ur−1+δgu,in Ω,ux>0,in Ω,ux=0,in ℝN∖Ω, where Ω⊂ℝN is a bounded Lipschitz domain with 0∈Ω, −Δs is a fractional Laplace operator, s∈0,1, N>2s, δ is a positive number, 2<r<rλ,s≡N+2s−2αλ/N−2s−2αλ+1, αλ∈0,N−2s/2 is a parameter depending on λ, 0<λ<ΛN,s, and ΛN,s=22sΓ2N+2s/4/Γ2N−2s/4 is the sharp constant of the Hardy–Sobolev inequality.

Being and Reason

2019 ◽  
Author(s):  
Martin Lin
Keyword(s):  
Sufficient Reason ◽  
Existence Of God ◽  
Principle Of Sufficient Reason ◽  
Existence And Nonexistence ◽  
New Interpretation ◽  
Necessary Existence

In Being and Reason, Martin Lin offers a new interpretation of Spinoza’s core metaphysical doctrines with attention to how and why, in Spinoza, metaphysical notions are entangled with cognitive, logical, and epistemic ones. For example, according to Spinoza, a substance is that which can be conceived through itself, and a mode is that which is conceived through another. Thus, metaphysical notions, substance and mode, appear to be defined through a notion that is either cognitive or logical, being conceived through. What are we to make of the intimate connections that Spinoza sees between metaphysical, cognitive, logical, and epistemic notions? Or between being and reason? Lin argues against idealist readings according to which the metaphysical is reducible to or grounded in something epistemic, logical, or psychological. He maintains that Spinoza sees the order of being and the order of reason as two independent structures that mirror one another. In the course of making this argument, he develops new interpretations of Spinoza’s notions of attribute and mode, and of Spinoza’s claim that all things strive for self-preservation. Lin also argues against prominent idealist readings of Spinoza according to which the Principle of Sufficient Reason is absolutely unrestricted for Spinoza and is the key to his system. He contends, rather, that Spinoza’s metaphysical rationalism is a diverse phenomenon and that the Principle of Sufficient Reason is limited to claims about existence and nonexistence which are applied only once by Spinoza to the case of the necessary existence of God.

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