[PDF] Top 20 4. Non-homogeneous Kirchhoff equation on $\mathbb{R}^3$
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4. Non-homogeneous Kirchhoff equation on $\mathbb{R}^3$
... [−∆u + V (x)u] = |u| p−2 u + g(x) in R 3 (1.1) Problems related to (1.1) model several physical and biological systems, where u describes a process, which depends on the average of itself, such as the ... See full document
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OBSERVATIONS ON THE NON HOMOGENEOUS EQUATION OF THE EIGHTHDEGREE WITH FIVE UNKNOWNS
... particular, homogeneous and non-homogeneous equations of higher degree have aroused the interest of numerous mathematicians since antiquity[1- ...determining non-trivial integral solution of ... See full document
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The existence and concentration of ground-state solutions for a class of Kirchhoff type problems in \({\mathbb{R}^{3}}\) involving critical Sobolev exponents
... We note that problem (.) with b = is motivated by the search for standing wave solutions for the nonlinear Schrödinger equation, which is one of the main subjects in nonlinear analysis. Different approaches ... See full document
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On the Non-Homogeneous Quintic Equation with Five Unknowns $X^4-Y^4=10 p^3 (Z^2-W^2)$
... quintic non-homogeneous equation with five unknowns represented by the Diophantine equation ( x 4 − y 4 ) ( = 10 z 2 − w 2 ) P 3 is analyzed for its patterns of ... See full document
6
The stability of solutions for the Fornberg–Whitham equation in \(L^{1}(\mathbb{R})\) space
... FW equation in the Besov space in both non-periodic and periodic cases and discussed the sharpness of continuity on the data-to-solution ...FW equation itself and some conclusions in [5] to derive ... See full document
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Nehari-type ground state solutions for asymptotically periodic fractional Kirchhoff-type problems in \(\mathbb{R}^{N}\)
... In the recent years, fractional and nonlocal operators arise in the description of vari- ous phenomena in the pure mathematical research and concrete real-world applications, such as fractional quantum mechanics [2, ... See full document
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Stoneley waves in a non homogeneous orthotropic granular medium under the influence of gravity
... The medium under consideration is discontinuous such as one composed numerous large or small grains. Unlike a continuous body, each element or grain cannot only trans- late but also rotate about its centre of gravity. ... See full document
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ON THE NON HOMOGENEOUS CUBIC EQUATION WITH FIVE UNKNOWNS EQUATION
... T 4. 16[ ( ,1) x a y a ( ,1) w a ( ,1) 4 CP a ,6 4 T 3, a 1] is a quintic integer ...T 3, a 8 CP a ,6 12( OH a ) 0( mod 3) 6. x (2 4 n , 2 2 n ) y (2 ... See full document
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The Surface Stresses on the Propagation of Elastic Waves
... in non-homogeneous ...“the non-homogeneity increases the phase velocity of the longer period ...in non- homogeneous medium seems to have been given by Honda ...period equation of ... See full document
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On the Non-Homogeneous Cubic Equation with Four Unknowns $(x-y)^2 = 2z^3+w^2$
... the non-homogeneous Diophantine cubic equation is an interesting concept as it can be seen from [1, 2, ...Diophantine equation with three and four unknowns are ...cubic equation with ... See full document
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Global existence, stability results and compact invariant sets for a quasilinear nonlocal wave equation on $mathbb{R}^{N}$
... wave equation with strong dissipation (see also [1, ...Also R. Ikehata [4] has shown that for sufficiently small initial data, global existence can be obtained, even when the influence of the source ... See full document
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Multiplicity of solutions for a quasilinear elliptic equation with \((p,q)\)-Laplacian and critical exponent on \(\mathbb{R}^{N}\)
... This paper is organized as follows. In Sect. 2, for the reader’s convenience, we describe the main mathematical tools which we shall use. The existence theorem for λ ∈ (0, λ ∗ ) is proved in Sect. 3 via the ... See full document
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On The Homogeneous Cubic Equation With Four Unknowns $(x^3+y^3)=7zw^2$
... representing homogeneous cubic with four unknowns for determining its infinitely many non-zero integral points, also a few interesting relations among the solutions are pres[r] ... See full document
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A variational inequality of Kirchhoff type in \(\mathbb{R}^{N}\)
... It is well known that the variational inequality is discussed in different ways in the case of regional bounded and unbounded. In [4], on the bounded interval (0, 1), a class of varia- tional inequalities of ... See full document
9
Multiple positive solutions to Kirchhoff equations with competing potential functions in \(\mathbb{R}^{3}\)
... Some early classical studies of Kirchhoff equations were those by Bernstein [4] and Po- hozaev [21]. Equation (1.2) received much attention after Lions [18] had proposed an ab- stract framework to the ... See full document
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On Homogeneous Cubic Diophantine equation with Four Unknowns $3(x^3+y^3) = 8zp^2$
... its non-zero distinct integral ...the equation under consideration are obtained the relations between the integer solutions and special numbers namely polygonal number and pyramidal number are ... See full document
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INTEGRAL SOLUTIONS OF NON- HOMOGENEOUS QUINTIC EQUATION WITH THREE UNKNOWNS
... is analyzed for its patterns of non-zero distinct integral solutions and three different methods of integral solutions are illustrated. Various interesting relations between the solutions and special numbers, ... See full document
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Existence, nonexistence, and multiplicity of solutions for the fractional \(p\&q\)-Laplacian equation in \(\mathbb{R}^{N}\)
... Up to now, it is worth noting that there is much attention on equations like (.), (.), and (.) with < m < r. From the papers mentioned, it is natural to ask whether the existence, nonexistence, and ... See full document
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On Solution of Homogeneous and Non-Homogeneous Differential Equation by Fractional Operators and N- Fractional Calculus Operator
... є R} is an abelian product group, which possesses (N ) 1 = N as the inverse ...of homogeneous and non-homogeneous Fuchs type equations by using N – fractional ... See full document
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Integral solution of the non-homogeneous Quintic Equation with Seven Unknowns .
... of Non-homogeneous Ternary quintic Equation, ax 2 by 2 ( a b z a b ) , , 5 0 , International Journal of Computational Engineering Research, ...Vol. 3(4), 45-50, April, 2013 ... See full document
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