We investigate the boundary value problem for biharmonic operators on Heisenberg group. The inherent features of Hn make it an appropriate environment studying symmetry rules and interaction analysis geometry with manifolds. goal this paper is to prove that a weak solution operator group exists. Our key tools are version Mountain Pass Theorem classical variational theory. This will be interest ...

Abstract In this paper, the existence of a solution for an anisotropic variable exponent system is obtained and proved under general hypotheses. By considering additional conditions, it multiplicity result. The proofs are based on application appropriated $L^{\infty }$ L ∞ </mml:ma...

We consider a kind of nonlinear systems on locally finite graph $$G=(V,E)$$ . prove via the mountain pass theorem that this has nontrivial ground state solution which depends parameter $$\lambda $$ with some suitable assumptions potentials. Moreover, we pay attention to concentration behavior these solutions and as \rightarrow \infty , converge corresponding Dirichlet problem. Finally, also pro...

In the paper, we study existence of weak solutions for a class new nonlocal problems involving p x -Laplacian operator. By using Ekeland’s variational principle and mountain pass theorem, prove that id="M3"> -Kirchhoff problem has at least two nontrivial sol...

Abstract In this paper, we study the initial boundary value problem for a class of higher-order n -dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from soil mechanics, heat conduction, optics. By mountain pass theorem first prove existence nonzero weak solution to static problem, is important basis evolution then based on method potential well global ...

We are concerned with the study of existence and multiplicity solutions for Dirichlet boundary value problems, involving $ ( p( m ), \, q( ) )- equation nonlinearity is superlinear but does not fulfil Ambrossetti-Rabinowitz condition in framework Sobolev spaces variable exponents a complete manifold. The main results proved using mountain pass theorem Fountain Cerami sequences. Moreover, an exa...

We deal with a weighted biharmonic problem in the unit ball of $\mathbb{R}^{4}$. The non-linearity is assumed to have critical exponential growth view Adam's type inequalities. weight $w(x)$ logarithm and potential $V$ positive continuous function on $\overline{B}$. It proved that there nontrivial weak solution this by mountain Pass Theorem. avoid loss compactness proving concentration result s...

We show how mountain pass methods can be used even when there is no mountain pass or saddle point geometry. The functional can grow on linking subsets. Applications are given.