Results 31 to 40 of about 671 (73)

Supplement a high-dimensional time fractional diffusion equation

Alexandria Engineering Journal, 2023
In this article, we discussed a high-dimensional time fractional diffusion equation which is used to write many nonlinear phenomena in three dimensional space diffusion processes.
Jian-Gen Liu, Fa-Zhan Geng, Xin Li
doaj  

On similarity solutions to (2+1)-dispersive long-wave equations

Journal of Ocean Engineering and Science, 2023
This work is devoted to get a new family of analytical solutions of the (2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth, and can be observed in an open sea or in wide channels.
Raj Kumar, Ravi Shankar Verma, Atul Kumar Tiwari   +2 more
doaj  

Symmetry in variational principles and applications [PDF]

, 2011
We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications to PDEs, fixed point theory and geometric analysis.
arxiv   +1 more source

Classical Lie symmetries and reductions of a nonisospectral Lax pair

, 2011
The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551).
Ablowitz M. J., Calogero F., Estévez P. G., Estévez P. G., Estévez P. G., Hirota R., Legaré M., Maccari A., Olver P. J., Painlevé P., Weiss J.   +10 more
core   +1 more source

Nontrivial solutions for resonance quasilinear elliptic systems

Advances in Nonlinear Analysis
We establish an Amann-Zehnder-type result for resonance systems of quasilinear elliptic equations with homogeneous Dirichlet boundary conditions, involving nonlinearities growing asymptotically (p,q)\left(p,q)-linear at infinity.
Borgia Natalino, Cingolani Silvia, Vannella Giuseppina   +2 more
doaj   +1 more source

Strong Comparison Principle for the Fractional p-Laplacian and Applications to Starshaped Rings

Advanced Nonlinear Studies, 2018
In the following, we show the strong comparison principle for the fractional p-Laplacian, i.e.
Jarohs Sven
doaj   +1 more source

An upper bound for the least energy of a sign-changing solution to a zero mass problem

Advanced Nonlinear Studies
We give an upper bound for the least possible energy of a sign-changing solution to the nonlinear scalar field equation −Δu=f(u),u∈D1,2(RN), $-{\Delta}u=f\left(u\right), u\in {D}^{1,2}\left({\mathrm{R}}^{N}\right),$ where N ≥ 5 and the nonlinearity f is
Clapp Mónica, Maia Liliane, Pellacci Benedetta   +2 more
doaj   +1 more source

Moving planes and sliding methods for fractional elliptic and parabolic equations

Advanced Nonlinear Studies
In this paper, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions.
Chen Wenxiong, Hu Yeyao, Ma Lingwei
doaj   +1 more source

Symmetry and uniqueness of nonnegative solutions of some problems in the halfspace [PDF]

Journal of Mathematical Analysis and Applications, 403 (2013), 215--233, 2012
We derive some 1-D symmetry and uniqueness or non-existence results for nonnegative solutions of some elliptic system in the halfspace $\R^N_+$ in low dimension. Our method is based upon a combination of Fourier series and Liouville theorems.
arxiv   +1 more source

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
doaj   +1 more source