On the Generalised Anti-Inverse Elasticity Rule: An Existence Result

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

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Existence result of entropy solution for some nonlinear parabolic problems under natural growths in Musielak spaces

Ricerche di Matematica ◽

10.1007/s11587-021-00591-3 ◽

2021 ◽

Author(s):

M. Bourahma ◽

J. Bennouna ◽

A. Benkirane

Keyword(s):

Existence Result ◽

Entropy Solution ◽

Parabolic Problems ◽

Nonlinear Parabolic Problems ◽

Nonlinear Parabolic

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Existence and Concentration Behavior of Solutions of the Critical Schrödinger–Poisson Equation in R3

Mathematics ◽

10.3390/math9050464 ◽

2021 ◽

Vol 9 (5) ◽

pp. 464

Author(s):

Jichao Wang ◽

Ting Yu

Keyword(s):

Poisson Equation ◽

Existence Result ◽

Critical Growth ◽

Singularly Perturbed ◽

Singularly Perturbed Problem ◽

Number Of Solutions ◽

Concentration Behavior ◽

The Relationship ◽

Concentration Phenomenon

In this paper, we study the singularly perturbed problem for the Schrödinger–Poisson equation with critical growth. When the perturbed coefficient is small, we establish the relationship between the number of solutions and the profiles of the coefficients. Furthermore, without any restriction on the perturbed coefficient, we obtain a different concentration phenomenon. Besides, we obtain an existence result.

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Nonlinear evolution problems with singular coefficients in the lower order terms

Nonlinear Differential Equations and Applications NoDEA ◽

10.1007/s00030-021-00698-4 ◽

2021 ◽

Vol 28 (4) ◽

Author(s):

Fernando Farroni ◽

Luigi Greco ◽

Gioconda Moscariello ◽

Gabriella Zecca

Keyword(s):

Lower Order ◽

Time Horizon ◽

Existence Result ◽

Nonlinear Evolution ◽

Order Term ◽

Time Behavior ◽

Infinite Time ◽

Singular Coefficient ◽

Singular Coefficients ◽

Lower Order Terms

AbstractWe consider a Cauchy–Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the solution in the case of the infinite–time horizon.

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Backwards Asymptotically Autonomous Dynamics for 2D MHD Equations

Discrete Dynamics in Nature and Society ◽

10.1155/2018/4948301 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11

Author(s):

Jiali Yu ◽

Wenhuo Su ◽

Dongmei Xu

Keyword(s):

Topological Property ◽

Existence Result ◽

Mhd Equations ◽

Pullback Attractors

We consider the backwards topological property of pullback attractors for the nonautonomous MHD equations. Under some backwards assumptions of the nonautonomous force, it is shown that the theoretical existence result for such an attractor is derived from an increasing, bounded pullback absorbing and the backwards pullback flattening property. Meanwhile, some abstract results on the convergence of nonautonomous pullback attractors in asymptotically autonomous problems are established and applied to MHD equations.

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RANDOM DIFFERENTIAL EQUATIONS WITH RANDOM DELAYS

Stochastics and Dynamics ◽

10.1142/s0219493711003358 ◽

2011 ◽

Vol 11 (02n03) ◽

pp. 369-388 ◽

Cited By ~ 30

Author(s):

M. J. GARRIDO-ATIENZA ◽

A. OGROWSKY ◽

B. SCHMALFUSS

Keyword(s):

Dynamical System ◽

Differential Equation ◽

Existence And Uniqueness ◽

Existence Result ◽

Random Dynamical System ◽

Random Delay ◽

Random Differential Equation ◽

Autonomous Case ◽

Random Differential Equations ◽

Uniqueness Of A Solution

We investigate a random differential equation with random delay. First the non-autonomous case is considered. We show the existence and uniqueness of a solution that generates a cocycle. In particular, the existence of an attractor is proved. Secondly we look at the random case. We pay special attention to the measurability. This allows us to prove that the solution to the random differential equation generates a random dynamical system. The existence result of the attractor can be carried over to the random case.

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