Related papers: Nontrival solution for nonlinear p(x)-Laplacian Di…
In this work, we study local minimizers of elliptic functionals with strong absorption terms and unbounded, sign-changing sources. These problems naturally interpolate between two classical free boundary problems: Bernoulli-type (cavity)…
In the present paper, we propose the investigation of variable-exponent, degenerate/singular elliptic equations in non-divergence form. This current endeavor parallels the by now well established theory of functionals satisfying nonstandard…
In this work we study the homogenization problem for nonlinear elliptic equations involving $p-$Laplacian type operators with sign changing weights. We study the asymptotic behavior of variational eigenvalues, which consist on a double…
In this paper we consider the following class of elliptic problems $$- \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,\,\, x\in \mathbb{R}^N$$ where $1<q<2<p<2^*-1= \frac{N+2}{N-2}$, $a_{\lambda}(x)$ is a sign-changing…
In this work, we establish the existence of solutions that change sign at low energy for a non-local weighted Kirchhoff problem in the set $\mathbb{R}^{N}, N>2$. The non-linearity of the equation is assumed to have exponential growth in…
Let $\mathcal{L}$ be a second-order linear elliptic operator with complex coefficients. We show that if the $L^p$ Dirichlet problem for the elliptic system $\mathcal{L}(u)=0$ in a fixed Lipschitz domain $\Omega$ in $\mathbb{R}^d$ is…
We are concerned with the nonexistence of sign-changing global weak solutions for a class of semilinear parabolic differential inequalities with convection terms in exterior domains. A weight function of the form $t^\alpha |x|^\sigma$ is…
We develop arguments on the critical point theory for locally Lipschitz functionals on Orlicz-Sobolev spaces, along with convexity and compactness techniques to investigate existence of solution of the multivalued equation $\displaystyle -…
A Dirichlet problem driven by the $(p,q)$-Laplace operator and an asymmetric concave reaction with positive parameter is investigated. Four nontrivial smooth solutions (two positive, one negative, and the remaining nodal) are obtained once…
In this paper we consider the following Dirichlet problem for the $p$-Laplacian in the positive parameters $\lambda$ and $\beta$: [{{array} [c]{rcll}% -\Delta_{p}u & = & \lambda h(x,u)+\beta f(x,u,\nabla u) & \text{in}\Omega u & = & 0 &…
We study a Dirichlet problem in the entire space for some nonlocal degenerate elliptic operators with internal nonlinearities. With very mild assumptions on the boundary datum, we prove existence and uniqueness of the solution in the…
We consider a model of fractional diffusion involving the natural nonlocal version of the $p$-Laplacian operator. We study the Dirichlet problem posed in a bounded domain $\Omega$ of ${\mathbb{R}}^N$ with zero data outside of $\Omega$, for…
We consider singular quasilinear elliptic systems with homogeneous Dirichlet boundary condition. Using Leray-Schauder topological degree, combined with the sub-supersolutions method and suitable truncation arguments, we establish the…
In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, non-symmetric divergence form operators. We show that a certain optimal…
We present a method of solving a nonlinear Dirichlet problem with discontinuous boundary data and we give a probabilistic representation of the solution using the nonlocal branching process associated with the nonlinear term of the…
In this paper we consider nonlinear elliptic PDEs of the type $$-\Delta_p u+a(x)|u|^{p-2}u=|u|^{p^*-2}u \qquad \mbox{ in }\Omega,$$ where $1<p<N$ and $p^*=Np/(N-p)$ is the critical Sobolev exponent, and allowing the asymptotic behavior of…
We consider the following critical semilinear nonlocal equation involving the fractional Laplacian $$ (-\Delta)^su=K(|x|)|u|^{2^*_s-2}u,\ \ \hbox{in}\ \ \mathbb{R}^N, $$ where $K(|x|)$ is a positive radial function, $N>2+2s$, $0<s<1$, and…
This paper is devoted to establishing results for semilinear elliptic boundary value problems where the solvability of problems subject to {\it No Flux} boundary conditions follows from the solvability of related {\it Dirichlet} boundary…
In this paper we study weighted singular $p$-Laplace equations involving a bounded weight function which can be discontinuous. Due to its discontinuity classical regularity results cannot be applied. Based on Nehari manifolds we prove the…
We prove existence of multiple radial solutions to the Dirichlet problem for nonlinear equations involving the mean curvature operator in Lorentz-Minkowski space and a nonlinear term of concave-convex type. Solutions are found using…