Multiplicity of solutions for a nonhomogeneous quasilinear elliptic problem with critical growth

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 apply the Nehari method combined with the concentration compactness theorem in an Orlicz-Sobolev framework. One of the difficulties in dealing with this kind of operator is the lost of homogeneity properties.Comment: arXiv admin note: text overlap with arXiv:1610.0465

Existence and multiplicity for perturbations of an equation involving Hardy inequality and critical Sobolev exponent in the whole R^N

In order to obtain solutions to problem {{array}{c} -\Delta u=\dfrac{A+h(x)} {|x|^2}u+k(x)u^{2^*-1}, x\in {\mathbb R}^N, u>0 \hbox{in}{\mathbb R}^N, {and}u\in {\mathcal D}^{1,2}({\mathbb R}^N), {array}. $h$ and $k$ must be chosen taking into account not only the size of some norm but the shape. Moreover, if $h(x)\equiv 0$, to reach multiplicity of solution, some hypotheses about the local behaviour of $k$ close to the points of maximum are needed.Comment: 23 page

Multiplicity results for a quasilinear equation with singular nonlinearity

For an open, bounded domain \Om in $\mathbb{R}^N$ which is strictly convex with $C^2$ boundary, we show that there exists a $\land>0$ such that the singular quasilinear problem \begin{eqnarray*} &-\delp u =\cfrac{\lambda}{u^{\del}}+u^q\,\,\mbox{in}\,\,\Om\\ &u=0\,\,\mbox{on}\,\,\partial\Om;\, \,\,u>0\,\,\mbox{in}\,\,\Om \end{eqnarray*} admits atleast two solution $u$ and $v$ in W^{1,p}_{loc}(\Om)\cap L^{\infty}(\Om) for any \del>0 and 0<\lam<\land provided $1<p<N$ and $p-1<q<\frac{p(N-1)}{N-p}-1$.\\ Moreover the solutions $u$ and $v$ are such that u^{\alp} and v^{\alp} are in W^{1,p}_0(\Om) for some \alp>0

Multiplicity and concentration behavior of solutions for a quasilinear problem involving NN-functions via penalization method

In this work, we study the existence, multiplicity and concentration of positive solutions for the following class of quasilinear problem: - \Delta_{\Phi}u + V(\epsilon x)\phi(\vert u\vert)u = f(u)\quad \mbox{in} \quad \mathbb{R}^{N}, where $\Phi(t) = \int_{0}^{\vert t\vert}\phi(s)sds$ is a N-function, $\Delta_{\Phi}$ is the $\Phi$-Laplacian operator, $\epsilon$ is a positive parameter, $N\geq 2$, $V : \mathbb{R}^{N} \rightarrow \mathbb{R}$ is a continuous function and $f : \mathbb{R} \rightarrow \mathbb{R}$ is a $C^{1}$-function.Comment: arXiv admin note: text overlap with arXiv:1506.0166

Stability of positive solutions to biharmonic equations on Heisenberg group

In this note, we establish the existence of a positive solution and its stability to the following problem \Delta_{\mathbb{H}^n}^2u=a(\xi)u-f(\xi,u)\text{ in }\Omega, \,\,\, u|_{\partial\Omega} = 0 =\left.\Delta_{\mathbb{H}^n} u|_{\partial\Omega}, on Heisenberg group.Comment: SOme remarks are added and few typos are corrected in this versio

Solution of Time-Fractional Korteweg-de Vries Equation in warm Plasma

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude ion-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.Comment: The paper is in tex format+3 figures in ep

On the existence and multiplicity of solutions for a fourth order discrete BVP

We investigate the existence and multiplicity of solutions for fourth order discrete boundary value problems via critical point theory

Time-Fractional KdV Equation Describing the Propagation of Electron-Acoustic Waves in plasma

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electron-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as the Earth's magnetotail region.Comment: about 17 pages + 6 figure

Solution to the Volterra integral equations of the first kind with piecewise continuous kernels in class of Sobolev-Schwartz distributions

Sufficient conditions for existence and uniqueness of the solution of the Volterra integral equations of the first kind with piecewise continuous kernels are derived in framework of Sobolev-Schwartz distribution theory. The asymptotic approximation of the parametric family of generalized solutions is constructed. The method for the solution's regular part refinement is proposed using the successive approximations method

Ion-Acoustic Waves in Unmagnitized Collisionless Weakly Relativistic Plasma using Time-Fractional KdV Equation

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves in unmagnitized collisionless weakly relativistic warm plasma. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.Comment: 16 pages+5 figure