Related papers: Multiple solutions for quasilinear elliptic system…
We generalize two embedding theorems and investigate the existence and multiplicity of nontrivial solutions for a $(p,q)$-Laplacian coupled system with perturbations and two parameters $\lambda_1$ and $\lambda_2$ on locally finite graph. By…
In this paper, we study the existence and multiplicity results of nontrivial positive solutions to a quasilinear elliptic equation in $\RN$, when $N\geq2$, as \begin{equation} \Lp…
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying…
We establish the existence of weak solutions of coupled systems of elliptic partial differential equations with quasimonotone nonlinearities in the domain interior and on the boundary. When the nonlinearities satisfy some monotonicity…
In this paper, we use bifurcation method to investigate the existence and multiplicity of one-sign solutions of the $p$-Laplacian involving a linear/superlinear nonlinearity with zeros. To do this, we first establish a bifurcation theorem…
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.
We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous…
We investigate a class of quasilinear elliptic system involving a nonhomogeneous differential operator which is introduced by C. A. Stuart [Milan J. Math. 79 (2011), 327-341] and depends on not only $\nabla u$ but also $u$. We show that the…
Existence of a generalized solution to a strongly singular convective elliptic equation in the whole space is established. The differential operator, patterned after the (p,q)-Laplacian, can be non-homogeneous. The result is obtained by…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
In this paper, we will prove the existence of infinitely many solutions to the following equation by utilizing the variational perturbation method \begin{equation*} -div(A(x,u)|\nabla u|^{p-2}\nabla u)+\frac{1}{p}A_{t}(x,u)|\nabla…
We establish the existence of multi-bump solutions for the following class of quasilinear problems $$ - \Delta_{ p(x) } u + \big( \lambda V(x) + Z(x) \big) u ^{ p(x)-1 } = f(x,u) \text{ in } \mathbb R^N, \, u \ge 0 \text{ in } \mathbb R^N,…
We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators…
The paper deals with the existence of non-radial solutions for an $N$-coupled nonlinear elliptic system. In the repulsive regime with some structure conditions on the coupling and for each symmetric subspace of rotation symmetry, we prove…
We show the existence of positive solutions for a class of singular elliptic systems with convection term. The approach combines pseudomonotone operator theory, sub and supersolution method and perturbation arguments involving singular…
In the present paper, we are concerned with entire radially symmetric solutions for a quasilinear system with phi{i}-Laplacian operator.
We consider a class of elliptic and parabolic problems, featuring a specific nonlocal operator of fractional-laplacian type, where integration is taken on variable domains. Both elliptic and parabolic problems are proved to be uniquely…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by elliptic equations with non-Lipschitz nonlinearities. Variational…
The aim of this paper is investigating the existence of one or more weak solutions of the coupled quasilinear elliptic system of gradient type \[ (P)\qquad \left\{ \begin{array}{ll} - {\rm div} (A(x, u)\vert\nabla u\vert^{p_1 -2} \nabla u)…