Existence of solutions for some non‐Fredholm integro‐differential equations with the bi‐Laplacian
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6721
Abstract: We prove the existence of solutions for some semilinear elliptic equations in the appropriate H4 spaces using the fixed‐point technique where the elliptic equation contains fourth‐order differential operators with and without Fredholm property, generalizing the… read more here.
Keywords: solutions non; integro differential; non fredholm; fredholm integro ... See more keywords
Existence of Solutions of Nonlinear and Non-local Fractional Boundary Value Problems
Sign Up to like & getrecommendations! Published in 2019 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-019-1388-9
Abstract: In this paper, we establish new results for non-local boundary value problems. In particular, we study a fractional differential equation where the associated integral equation has a kernel that is not bounded above and changes… read more here.
Keywords: existence solutions; boundary value; solutions nonlinear; non local ... See more keywords
Existence of Solutions for Some Nonlinear Elliptic Equations in Musielak Spaces with Only the Log-Hölder Continuity Condition
Sign Up to like & getrecommendations! Published in 2019 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-019-1466-z
Abstract: We study the existence of solutions for some nonlinear elliptic problems with $$L^1$$L1 data in Musielak spaces; we assume that the Musielak function satisfies only the log-Hölder continuity condition. read more here.
Keywords: solutions nonlinear; lder continuity; musielak spaces; nonlinear elliptic ... See more keywords
Nonlinear filters in topology optimization: existence of solutions and efficient implementation for minimum compliance problems
Sign Up to like & getrecommendations! Published in 2017 at "Structural and Multidisciplinary Optimization"
DOI: 10.1007/s00158-016-1553-8
Abstract: Material distribution topology optimization problems are generally ill-posed if no restriction or regularization method is used. To deal with these issues, filtering procedures are routinely applied. In a recent paper, we presented a framework that… read more here.
Keywords: topology; topology optimization; minimum compliance; existence solutions ... See more keywords
Existence of Solutions to Shallow Lake Type Optimal Control Problems
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Optimization Theory and Applications"
DOI: 10.1007/s10957-020-01660-7
Abstract: We consider the optimal control problem associated with a general version of the well known Shallow Lake model, and we prove the existence of an optimum in the class of all positive, locally integrable functions… read more here.
Keywords: solutions shallow; control; optimal control; existence solutions ... See more keywords
Existence of solutions for a critical fractional Kirchhoff type problem in ℝN
Sign Up to like & getrecommendations! Published in 2017 at "Science China Mathematics"
DOI: 10.1007/s11425-015-0792-2
Abstract: This paper concerns with the existence of solutions for the following fractional Kirchhoff problem with critical nonlinearity: $${\left( {\int {\int {_{{\mathbb{R}^{2N}}}\frac{{{{\left| {u\left( x \right) - u\left( y \right)} \right|}^2}}}{{{{\left| {x - y} \right|}^{N + 2s}}}}dxdy}… read more here.
Keywords: left right; solutions critical; fractional kirchhoff; problem ... See more keywords
Existence of Solutions for a Functional Integro-Differential Equation with Infinite Point and Integral Conditions
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Applied and Computational Mathematics"
DOI: 10.1007/s40819-019-0691-2
Abstract: In this article, we study the existence of solutions for two initial value problems of the functional integro-differential equation with nonlocal infinite-point and integral conditions. We study the continuous dependence of the solution. As some… read more here.
Keywords: differential equation; integro differential; infinite point; functional integro ... See more keywords
Existence of solutions to the Orlicz–Minkowski problem
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2019.01.004
Abstract: Abstract In this paper the Orlicz–Minkowski problem, a generalization of the classical Minkowski problem, is studied. Using the variational method, we obtain a new existence result of solutions to this problem for general measures. read more here.
Keywords: minkowski problem; orlicz minkowski; existence solutions; problem ... See more keywords
Time-dependent singularities in semilinear parabolic equations: Existence of solutions
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2017.07.016
Abstract: Abstract We study the existence of solutions of the semilinear parabolic equation ∂ t u − Δ u = u p + Λ in D ′ ( R N × I ) . Here N… read more here.
Keywords: semilinear parabolic; time dependent; singularities semilinear; parabolic equations ... See more keywords
The existence of solutions for nonlinear elliptic equations: Simple proofs and extensions of a paper by Y. Shi
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2022.02.014
Abstract: The paper [Shi19] uses the Craig-Wayne-Bourgain method to construct solutions of an elliptic problem involving parameters. The results of [Shi19] include regularity assumptions on the perturbation and involve excluding parameters. The paper [Shi19] also constructs… read more here.
Keywords: paper; ill posed; problem; elliptic equations ... See more keywords
Existence of solutions for systems arising in electromagnetism
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.123898
Abstract: Abstract In this paper, we study the following p ( x ) -curl systems: { ∇ × ( | ∇ × u | p ( x ) − 2 ∇ × u ) + a… read more here.
Keywords: electromagnetism; existence; solutions systems; arising electromagnetism ... See more keywords