Global solutions to semilinear parabolic equations driven by mixed local–nonlocal operators
Bulletin of the London Mathematical Society, Volume 57, Issue 1, Page 265-284, January 2025.Abstract We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local–nonlocal operator L=−Δ+(−Δ)s$\mathcal {L}= -\Delta +(-\Delta)^s$, with a power‐like source term. We show that the so‐called Fujita phenomenon holds, and the critical value is exactly the same as for the fractional Laplacian.
Stefano Biagi +2 more
wiley +1 more source
Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems
Electronic Journal of Differential Equations, 1999 When using calculus of variations to study nonlinear elliptic boundary-value problems on unbounded domains, the Palais-Smale condition is not always satisfied.
Chao-Nien Chen, Shyuh-Yaur Tzeng
doaj
Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian
Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℝN, where N ≥ 3, F represents the primitive function of f, f∈CR;R is a function that fulfils the general Berestycki–Lions conditions, ΔD denotes the Laplacian operator on Ω with zero Dirichlet boundary conditions
Sarah Abdullah Qadha +4 more
wiley +1 more source
A posteriori error estimation and adaptivity for temporal multiscale problems
PAMM, Volume 24, Issue 4, December 2024.Abstract In science and engineering, problems over multiple scales in time often arise. Two examples are material damage in oscillating structures or plaque growth in pulsating blood vessels. Here the long term effects are of interest but they depend on the coupled fast‐changing physical processes which must be taken into account.
Leopold Lautsch, Thomas Richter
wiley +1 more source
Electronic Journal of Differential Equations, 2016 In this article, we study a class of semilinear elliptic equations involving Hardy-Sobolev critical exponents and Hardy-Sobolev-Maz'ya potential in a bounded domain. We obtain the existence of positive solutions using the Mountain Pass Lemma.
Rui-Ting Jiang, Chun-Lei Tang
doaj
Ground states of semilinear elliptic equations
, 2020 Comments are ...
Caju, Rayssa +3 more
openaire +2 more sources
Sub-supersolution theorems for quasilinear elliptic problems: A variational approach
Electronic Journal of Differential Equations, 2004 This paper presents a variational approach to obtain sub - supersolution theorems for a certain type of boundary value problem for a class of quasilinear elliptic partial differential equations.
Vy Khoi Le, Klaus Schmitt
doaj
Unique continuation property and local asymptotics of solutions to fractional elliptic equations [PDF]
, 2013 Asymptotics of solutions to fractional elliptic equations with Hardy type potentials is studied in this paper. By using an Almgren type monotonicity formula, separation of variables, and blow-up arguments, we describe the exact behavior near the ...
Fall, Mouhamed Moustapha, Veronica Felli
core
Computation of radial solutions of semilinear equations
Electronic Journal of Qualitative Theory of Differential Equations, 2007 We express radial solutions of semilinear elliptic equations on $R^n$ as convergent power series in $r$, and then use Pade approximants to compute both ground state solutions, and solutions to Dirichlet problem.
Philip Korman
doaj +1 more source
Mathematical modeling of optimal processes, described by semilinear equations of elliptic type with discontinuous coefficients and solutions [PDF]
, 2022 openalex +1 more source