Related papers: Sign changing solution for a double phase problem …
In this paper we study a singular Finsler double phase problem with a nonlinear boundary condition and perturbations that have a type of critical growth, even on the boundary. Based on variational methods in combination with truncation…
In this paper, we consider a fractional p-Laplacian system with both concave-convex nonlinearities and sign-changing weight functions in bounded domains. With the help of the Nehari\ manifold, we prove that the system has at least two…
We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at…
We consider a nonautonomous semilinear elliptic problem where the power nonlinearity is multiplied by a discontinuous coefficient that equals one inside a bounded open set $\Omega$ and it equals minus one in its complement. In the slightly…
In this paper we study quasilinear elliptic systems driven by so-called double phase operators and nonlinear right-hand sides depending on the gradients of the solutions. Based on the surjectivity result for pseudomonotone operators we…
In this paper we study quasilinear elliptic equations driven by the double phase operator involving a Choquard term of the form \begin{align*} -\mathcal{L}_{p,q}^{a}(u) + |u|^{p-2}u+ a(x) |u|^{q-2}u = \left( \int_{\mathbb{R}^N} \frac{F(y,…
In this paper we are concerned with some $p$-Kirchhoff type problems involving sign-changing weight functions. We prove the existence of multiple positive solutions of the problem via the Nehari manifold approach.
It is established some existence and multiplicity of solution results for a quasilinear elliptic problem driven by $\Phi$-Laplacian operator. One of these solutions is built as a ground state solution. In order to prove our main results we…
In this paper, we study the multiplicity of positive solutions for the p-Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive…
We investigate the existence of nodal (sign-changing) solutions to the Dirichlet problem for two-parametric family of partially homogeneous $(p,q)$-Laplace equations $-\Delta_p u -\Delta_q u=\alpha |u|^{p-2}u+\beta |u|^{q-2}u$ where $p \neq…
We study the existence of positive solutions for a class of double phase Dirichlet equations which have the combined effects of a singular term and of a parametric superlinear term. The differential operator of the equation is the sum of a…
We establish the existence and nonexistence of entire solutions to a semilinear elliptic problem whose nonlinearity is the critical power multiplied by a function that takes the value 1 in an open bounded region and the value -1 in its…
In this paper, we are concerned with the quasilinear Schr\"{o}dinger equation \begin{equation*} -\Delta u+V(x)u-u\Delta(u^2)=g(u),\ \ x\in \mathbb{R}^{N}, \end{equation*} where $N\geq3$, $V$ is radially symmetric and nonnegative, and $g$ is…
We prove that a class of superlinear indefinite problems with homogeneous Neumann boundary conditions admits an arbitrarily high number of positive solutions, provided that the parameters of the problem are adequately chosen. The…
\noi In this article, we study the existence of non-negative solutions of the following polyharmonic Kirchhoff type problem with critical singular exponential nolinearity $$ \quad \left\{ \begin{array}{lr} \quad…
In this paper, we deal with equations of variational form which Nahari manifolds can contain more than two different types of critical points. We introduce a method of separating critical points on the Nahari manifold, based on the use of…
We study the existence of bound and ground states for a class of nonlinear elliptic systems in $\mathbb{R}^N$. These equations involve critical power nonlinearities and Hardy-type singular potentials, coupled by a term containing up to…
We prove new existence results for a Nonlinear Helmholtz equation with sign-changing nonlinearity of the form $$ - \Delta u - k^{2}u = Q(x)|u|^{p-2}u, \quad u \in W^{2,p}(\mathbb{R}^{N}) $$ with $k>0,$ $N \geq 3$, $p \in…
We study the existence, multiplicity and regularity results of non-negative solutions of following doubly nonlocal problem: $$ (P_\la) \left\{ \begin{array}{lr}\ds \quad (-\Delta)^{s_1}u+\ba (-\Delta)^{s_2}_{p}u = \la a(x)|u|^{q-2}u+…
It is established existence of bound and ground state solutions for quasilinear elliptic systems driven by (\phi 1, \phi 2)-Laplacian operator. The main feature here is to consider quasilinear elliptic systems involving both nonsingular…