Related papers: Sign changing solution for a double phase problem …
In this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such…
This article consists of study of anisotropic double phase problems with singular term and sign changing subcritical as well as critical nonlinearity. Seeking the help of well known Nehari manifold technique, we establish existence of at…
In this paper we study quasilinear elliptic equations driven by the double phase operator and a right-hand side which has the combined effect of a singular and of a parametric term. Based on the fibering method by using the Nehari manifold…
Results on existence and multiplicity of solutions for a nonlinear elliptic problem driven by the $\Phi$-Laplace operator are established. We employ minimization arguments on suitable Nehari manifolds to build a negative and a positive…
In this paper we first introduce an innovative equivalent norm in the Musielak-Orlicz Sobolev spaces in a very general setting and we then present a new result on the boundedness of the solutions of a wide class of nonlinear Neumann…
This paper is mainly concerned with the existence of ground state sign-changing solutions for a class of second order quasilinear elliptic equations in bounded domains which derived from nonlinear optics models. Combining a non-Nehari…
In this paper, we study a class of double phase systems which contain the singular and mixed nonlinear terms. Unlike the single equation, the mixed nonlinear terms make the problem more complicate. The geometry of the fibering mapping has…
In this paper we study quasilinear elliptic equations driven by the double phase operator along with a reaction that has a singular and a parametric superlinear term and with a nonlinear Neumann boundary condition of critical growth. Based…
This paper is concerned with multiplicity results for parametric singular double phase problems in $\mathbb{R}^N$ via the Nehari manifold approach. It is shown that the problem under consideration has at least two nontrivial weak solutions…
We are looking for solutions to nonlinear Schr\"odinger-type equations of the form $$ (-\Delta)^{\alpha / 2} u (x) + V(x) u(x) = h (x,u(x)), \quad x \in \mathbb{R}^N, $$ where $V : \mathbb{R}^N \rightarrow \mathbb{R}$ is an external…
We prove the existence of one positive, one negative, and one sign-changing solution of a $p$-Laplacian equation on $\mathbb{R}^N$, with a $p$-superlinear subcritical term. Sign-changing solutions of quasilinear elliptic equations set on…
In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and a nonlinear term of subcritical growth. Under very general assumptions on the data,…
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…
This paper is dedicated to studying the existence of nontrivial positive solutions for a Kirchhoff-type problem with sign change nonlinearities and a singular term, Using the Nehari manifold and EkelandS variational principle we prove that…
In this paper, we study a class of quasilinear elliptic equations involving both local and nonlocal operators with variable exponents. The problem exhibits singular nonlinearities along with a subcritical superlinear growth term and a…
In this paper, we study the multiplicity of nonnegative solutions for mixed local and non-local problem involving critical nonlinearity with sign changing weight. Using Nehari manifold method and fibering map analysis, we have shown…
In this article, we study the existence and multiplicity of non-negative solutions of following $p$-fractional equation: $$ \quad \left\{\begin{array}{lr}\ds \quad - 2\int_{\mb R^n}\frac{|u(y)-u(x)|^{p-2}(u(y)-u(x))}{|x-y|^{n+p\al}} dxdy =…
In this present paper, we investigate a new class of singular double phase $p$-Laplacian equation problems with a $\psi$-Hilfer fractional operator combined from a parametric term. Motivated by the fibering method using the Nehari manifold,…
We consider a double phase problem driven by the sum of the $p$-Laplace operator and a weighted $q$-Laplacian ($q<p$), with a weight function which is not bounded away from zero. The reaction term is $(p-1)$-superlinear. Employing the…
We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions; the boundary data is assumed to have finite number of relative maximum and minimum values. We are interested in certain…